MATH 540 Final Exam (3 different VERSIONS)

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MATH 540 Final Exam (3 different VERSIONS)

VERSION 1

Validation of a simulation model occurs when the true steady state average results have been reached

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables

In a total integer model, all decision variables have integer solution values

Fractional relationships between variables are not permitted in the standard form of a linear program

A cycle is an up and down movement in demand that repeats itself in less than 1 year

In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs

The probability of observing x successes in a fixed number of trials is a problem related to

Using the minimax regret criterion to make a decision, you

In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?

In linear programming problems, multiple optimal solutions occur

Using the maximin criterion to make a decision, you

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint?

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?

The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly profit?

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively.  The investor has up to $50,000 to invest.

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively.  The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased.  Which constraint is correct?

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

A professor needs help from 3 student helpers to complete 4 tasks.  The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios.  The estimated time for each student to do each task is given in the matrix below.

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport.  At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels.  What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note:  please provide your answer to 2 places past the decimal point, rounding as appropriate.

Professor Dewey  would like to assign grades such that 15% of students receive As.  If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

__________ moving averages react more slowly to recent demand changes than do __________ moving averages.

Consider the following graph of sales.

For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

Ford’s Bed & Breakfast  breaks even if they sell 50 rooms each month.  They have a fixed cost of $6500 per month.  The variable cost per room is $30.  For this model to work, what must be the revenue per room?  (Note: The answer is a whole dollar amount.   Give the answer as a whole number, omitting the decimal point.  For instance, use 105 to write $105.00). 

Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200.  The variable cost per room is $75.  How many rooms do they have to sell each month to break even?  (Note: The answer is a whole number.   Give the answer as a whole number, omitting the decimal point.  For instance, use 12 for twelve rooms). 

Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university?   (Note:  write your answer as a probability, with two decimal places.  If necessary, round to two decimal places.  For instance, a probability of 0.252 should be written as 0.25). 

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.

Let’s say that a life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75th
birthday?   Note:  Round your answer, if necessary, to two places after the decimal.  Please express your answer with two places after the decimal.

Ms. James is considering four different opportunities, A, B, C, or D.  The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).  Note:  Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000).  Round to the nearest whole number, if necessary. 

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).  Note:  Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000).  Round to the nearest whole number, if necessary.

The following sales data are available for 2003-2008 :

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer

VERSION 2

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected

Fractional relationships between variables are not permitted in the standard form of a linear program

In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.

In a total integer model, all decision variables have integer solution values

A cycle is an up and down movement in demand that repeats itself in less than 1 year

Using the maximin criterion to make a decision, you

Events that cannot occur at the same time in any trial of an experiment are

Using the minimax regret criterion to make a decision, you

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow

The probability of observing x successes in a fixed number of trials is a problem related to

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function?

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:

Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2

What is the sensitivity range for the third constraint, y ≥ 2?

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest.
An appropriate part of the model would be

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?

The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6?

Professor Truman would like to assign grades such that 10% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are:

Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

__________ moving averages react more slowly to recent demand changes than do __________ moving averages.

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

Carter’s Bed & Breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $1050 per month and the revenue they receive from each booked room is $150. What is the variable cost per occupied room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00).

Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200. The variable cost per room is $75. How many rooms do they have to sell each month to break even? (Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms).

Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “$” sign. For instance, for five dollars, write your answer as 5.00).

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table

Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer

Let’s say that a life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75th
birthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal

Ms. Hegel is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary

The following sales data are available for 2003-2008

Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer

VERSION 3

In general, an increase in price increases the break even point if all costs are held constant.

The feasible solution area contains infinite solutions to the linear program

A change in the value of an objective function coefficient will always change the value of the optimal solution.

When using a linear programming model to solve the “diet” problem, the objective is generally to maximize nutritional content.

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 can not be selected.

In a transshipment problem, items may be transported from destination to destination and from source to source.

The events in an experiment are mutually exclusive if only one can occur at a time

The minimax criterion minimizes the maximum payoff.

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

A cycle is an up and down movement in demand that repeats itself in less than 1 year.

A bed and breakfast even every month if they book 30 rooms over the course of a month.  Their fixed cost is $6000 per month and the revenue they receive from each booked room is $180.  What is the variable cost per occupied room?

If the price decreases but fixed and variable costs do not change, the break even point  

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem: 

Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to        8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2

Compared to blending and product mix problems, transportation problems are unique because

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint

The Wiethoff Company has a contract to produce garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used

The assignment problem constraint x31+x32+x33+x34 ≤ 2 means

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C

Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot.  Assume also that this time is normally distributed with a standard deviation of 2 minutes. What percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow

A bakery is considering hiring another clerk to better serve customers.  To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals.  Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed

For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of

Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45.  Find the break-even point

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)

Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.

MAX Z = 5×1 + 8×2
s.t.             x1 + x2 ≤ 6
5×1 + 9×2 ≤ 45
x1, x2 ≥ 0 and integer

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer

An investor is consider 4 different opportunities, A, B, C, or D.  The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? Do not include the dollar “$” sign with your answer

The following sales data are available for 2003-2008