Question Details

MAT 540
FINAL EXAM

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables. 
  cycle is an up and down movement in demand that repeats itself in less than 1 year.
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.
n an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
a transshipment problem, items may be transported from destination to destination and from source to source. 
 	In linear programming problems, multiple optimal solutions occur
Answer
 	An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.
Answer
The probability of observing x
successes in a fixed number of trials is a problem related to
Events that cannot occur at the same time in any trial of an experiment are:
In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?
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?
Answer		
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?
The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:  
 
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:
Answer			
Compared to transportation LP problems, assignment problems are unique because
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 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?
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.
5 out of 5 points
	
 	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:
Answer			
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.
 
                         
 
Which of the following constraints represents the assignment for student A?

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.)
Answer			
5 out of 5 points
	
 	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.)
Answer			
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?
Answer
__________ moving averages react more slowly to recent demand changes than do __________ moving averages.
sider the following graph of sales. 
 
                       
 
Which of the following characteristics is exhibited by the data?
 	In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
Answer
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).  	Suppose that a production process requires a fixed cost of $50,000. The variable cost per unit is $10 and the revenue per unit is projected to be $50.  Find the break-even point.
 
Answer
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).      	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.
 
Answer

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.
Klein 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 (%)
Partner's Choice	$0.20	45	20
Feline Excel	$0.15	15	30

 
Klein 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, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.
 
Max Z =         x1 + 6x2 
Subject to:      17x1 + 8x2 ≤ 136 
                       3x1 + 4x2 ≤ 36 
                       x1, x2 ≥ 0 and integer
0 out of 5 points
	
 	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 75th birthday?   Note:  Round your answer, if necessary, to two places after the decimal.  Please express your answer with two places after the decimal.  
 
Answer			
Mr. Sartre 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	38	25	33	10
B	10	15	20	85
C	20	100	20	-25
D	25	25	100	25

 
 
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
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 : 
 
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
Answer			
 	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.
 
Answer