MAT/540 MAT540 MAT 540 Week 11 FINAL EXAM

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. 

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?

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.

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.
 
 

 
 
Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable

In linear programming problems, multiple optimal solutions occur

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

An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.

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.
 
           
 
If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

Using the maximin criterion to make a decision, you

Compared to transportation LP problems, assignment problems are unique because

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively.  Five essential ingredients are contained in the feed, shown in the table below.  The table also shows the minimum daily requirements of each ingredient.
 

 
The constraint for ingredient 3 is:

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)
 
Sensitivity Report:

 
 
A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.
 

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.
 

 
Formulation:
Let                   x = number of tractors produced per period
                        y = number of lawn mowers produced per period
MAX 30x + 30y
subject to   2 x + y       ≤ 60
                  2 x + 3y     ≤ 120
                     x ≤ 45
                    x, y  ≥ 0
The graphical solution is shown below.
 

 
 
 
What is the shadow price for fabrication?  Write your answers with two significant places after the decimal and do not include the dollar “$” sign.
 

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 storage space constraint?

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). 

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). 

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).     
 

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 68 years and a standard deviation of 4 years. What proportion of the plan participants are expected to survive to see their 75^th birthday?   Note:  Round your answer, if necessary, to two places after the decimal.  Please express your answer with two places after the decimal. 
 

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.
 
MAX Z = 5x1 + 8x2
s.t.             x1 + x2 ≤ 6
                  5x1 + 9x2 ≤ 45
                  x1, x2 ≥ 0 and integer

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.
 
                              
 
The constraint that represents the quantity demanded by Customer B is:

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?

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?

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. 
 
 
                       

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

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

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

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

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

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

Kalamazoo 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:
 

     
 
Kalamazoo Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note:  Please write your answers with two significant places after the decimal and do not include the dollar “$” sign.  For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
 

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.
 

 
 
 
 
 
 
 
 
 
 
Suppose the next three random numbers were .18, .89 and .67.  How many customers would have arrived during this 30-minute period?

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.

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

Recent past demand for product DEF is given in the following table.
 

 
The forecasted demand for May, June, July and August were 17, 18, 20  and 24 respectively. Determine the value of MAD. Note:  Please express the result as a number with 2 decimal places.  If necessary, round your result accordingly.  For instance, 9.146, should be expressed as 9.15

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.

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?