# MATHEMATICS

33.       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

Cat Food                     Cost/oz                       protien (%)                 fat (%)

Meow Munch              \$0.20                                       30                    10

Feline Feed                  \$0.15                                       15                    30

Kitty 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

34.       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

35.       Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3.  Find P(x ≤ 6).  Note:  Round your answer, if necessary, to two places after the decimal.  Please express your answer with two places after the decimal

36.       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

37.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

38.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.

39.       The following sales data are available for 2003-2008 :

 Year Sales Forecast 2003 7 7 2004 8 8.5 2005 12 10.5 2006 14 13 2007 16 15 2008 18 16

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

40.       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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