Question Details

MAT 540
WEEK 11
 
Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.
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A cycle is an up and down movement in demand that repeats itself in less than 1 year.
 
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Fractional relationships between variables are not permitted in the standard form of a linear program.
 
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In a total integer model, all decision variables have integer solution values. 
 
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If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint. 
 
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In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
 
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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 conservative (maximin) strategy is:
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In linear programming problems, multiple optimal solutions occur
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Using the minimax regret criterion to make a decision, you
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Using the maximin criterion to make a decision, you
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The probability of observing x
successes in a fixed number of trials is a problem related to
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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?
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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. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?
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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?
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The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:  
 
The Answer Report: 
 
 
The Sensitivity Report:  
 
 
Which additional resources would you recommend to be increased?
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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 demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.
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Compared to transportation LP problems, assignment problems are unique because
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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 the constraint that indicates they have to use at least three of the five machines in their production.
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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.
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The assignment problem constraint x31+x32+x33+x34 ≤ 2 means
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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 supplied by DC 1 is:
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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.)
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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:
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In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
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__________ moving averages react more slowly to recent demand changes than do __________ moving averages.
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For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:
 
                          
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Consider the following graph of sales. 
 
                       
 
Which of the following characteristics is exhibited by the data?
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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).     
 
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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). 
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Ford- 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). 
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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 assembly? Write your answers with two significant places after the decimal and do not include the dollar “$” sign.
 
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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:
 
 
 
 
 
 
 
 
 
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$7
 Regular =
291.67
0.00
50
70
20
$C$7
Super =
133.33
0.00
75
50
43.75
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$E$3
Assembly (hr/unit)
563.33
0.00
600
1E+30
36.67
$E$4
Paint (hr/unit)
300.00
33.33
300
39.29
175
$E$5
Inspect (hr/unit)
100.00
145.83
100
12.94
40

 
If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.
 
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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- 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: 
 
Cat Food
Cost/oz
protien (%)
fat (%)
Pet's Choice
0.35
40
15
Feline Chow
0.32
20
30

      
 
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
 
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Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.
 
Max Z =         x1 + 6x2 
Subject to:      17x1 + 8x2 ≤ 136 
                       3x1 + 4x2 ≤ 36 
                       x1, x2 ≥ 0 and integer
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Let- 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.  
 
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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.
 
 
Investment
Economic Conditions

Poor
(S1)
Average
(S2)
Good
(S3)
Excellent
(S4)
A
18
25
50
80
B
19
100
50
75
C
100
26
120
60
D
20
27
50
240

 
 
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
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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.  
 
 
 
                         
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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.  
 
 
                         
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The following sales data are available for 2003-2008 : 
 
Year
Sales
Forecast
2003
7
9
2004
12
10
2005
14
15
2006
20
22
2007
16
18
2008
25
21

 
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
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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.
 
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