AGEC 622 LP Homework 4 new

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Texas A&M University *

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622

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Business

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Feb 20, 2024

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AGEC 622 LP Homework 4 Total Points Possible : 130 points 1. (30 pts) Suppose you are in charge of the Contgill grain and you have the problem of managing company storage. Further, you know today: a) Grain can be sold for $2.00/bu. and you think the price will go up by 5 per bushel per month the next 7 months, then down by 10 for the subsequent four months. b) It costs you 2/month/bu. to keep the grain. c) Eight months from now your chairman has said 10% of the grain you have on hand must be committed to PL 480, for which you are not reimbursed. You must commit at least 50,000 bushels. d) You have 10,000,000 bushels of grain on hand. e) 0.1% of the grain spoils each month. 1) (20 pts) Set up a profit maximizing LP. 2) (10 pts) Interpret your results (objective function, decision variables (2), shadow prices (2) and reduced costs (2)) 2. (40 pts) Suppose you are consulting with an investor to determine how much of 4 stocks to buy. From previous years' experience, the investor has observed the following data on returns per five hundred dollars invested from each of the four stocks: Ob s Stock 1 Stock 2 Stock 3 Stock 4 1 55 45 35 20 2 60 70 28 20 3 18 28 30 22 4 -30 42 12 19 5 50 15 40 21 6 60 40 22 18 7 41 30 35 20 8 16 19 36 20 The investor has 500,000 to invest.
a. (20 pts) Formulate the investor's problem using the E-V criterion. Write down the mathematical notation. b. (20 pts) Solve it for the following 6 risk aversion coefficients and explain why the solutions change. Rap= 0; 0.01 ; 0.1 ; 1 ; 1.5 ; 2 3. (20 pts.) The Fribsky Company is considering adding three product lines to include producing milk (X 1 ), yogurt (X 2 ) and ice cream (X 3 ). are the potential 𝑌 1 , 𝑌 2 , ?𝑛? 𝑌 3 machine purchase decisions the company can make. A consultant suggests that the Company faces the following Mixed Integer Programming problem: …………(1) …………(2) …………(3) …………(4) …………(5) , …………(6) …………(7) 𝑌 1 , 𝑌 2 , ?𝑛? 𝑌 3 ??? ?𝑖𝑛??𝑦 𝑣??𝑖??𝑙?? Explain: a) (5 pts.) what would the coefficients and represent? 𝐹 1 𝑀 1 b) (5 pts.) the economic meaning of constraint (2) (the relationship between X2 and Y2) c) (5 pts.) the economic meaning of constraint (3) (the relationship among X3, Y1, and Y3) d) (5 pts.) the effects of constraints and . 4. (40 pts) Skylar has a beverage packing company packing canned soda into varying 36-can packages. The packing process consumes labor, and it is limited by the machine’s capacity. Assume the capacity of the packing machine is 6000 packages. The machine can switch to
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