1 1m1 1ms1130 month 1 demand mens bikes 2 1w1 1ws195

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Exploring Microeconomics
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Chapter 7 / Exercise 6
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1) 1M1-1MS1=130 Month 1 Demand Men’s bikes 2) 1W1-1WS1=95 Month 1 Demand Women’s bikes 3) 1M2+1MS1-1MS2=200 Month 2 Demand Men’s bikes 4) 1W2+1WS1-1WS2=150 Month 2 Demand Women’s bikes 5) 1MS2>25 Inventory requirement Men’s 6) 1WS2>25 Inventory requirement Women’s 7) 3.5M1+2.6W1>900 Month 1 labor Minimum 8) 3.5M1+2.6W1<1100 Month 1 labor Maximum 9) 3.5M1+2.6W1-3.5M2-2.6W2<100 Month 2 labor 10) -3.5M1-2.6W1+3.5M2+2.6W2<100 Month 2 labor Objective Function Value = 67156.029 Variable Value Reduced Costs M1 192.929 0.000 W1 95.000 0.000 M2 162.071 0.000 W2 175.000 0.000 MS1 62.929 0.000 WS1 0.000 0.017 MS2 25.000 0.000 WS2 25.000 0.000 Constraint Slack/Surplus Dual Prices 1 0.000 -118.800 2 0.000 -89.109 3 0.000 -121.200 4 0.000 -90.891 5 0.000 -123.600 6 0.000 -92.691 7 22.250 0.000 8 177.750 0.000 9 200.000 0.000 10 0.000 0.343 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit M1 117.600 120.000 120.023 W1 89.983 90.000 No Upper Limit M2 119.977 120.000 122.400 W2 -2.691 90.000 90.017 MS1 0.000 2.400 2.423 WS1 1.783 1.800 No Upper Limit MS2 -121.200 2.400 No Upper Limit WS2 -90.891 1.800 No Upper Limit
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Exploring Microeconomics
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Chapter 7 / Exercise 6
Exploring Microeconomics
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5 8. As part of a settlement for a class action lawsuit, Cheney-Burton must provide sufficient cash to pay out 750 thousand dollars over the next five years (including the current year). Annual payments, as outlined by the judge in the case, must be made at the beginning of each year. The initial payment will be made in cash with the payments over the next four years made from interest on two types of Government Securities (purchased at the beginning of year one only) and one year risk-free securities. Funds not invested in Government securities will be placed in one year risk-free security investments. Interest is paid annually for all investment alternatives. The current price of both Government Securities is $1,000 (par value = $1,000). The LP solution is provided below (each question is worth two points) 8a. How much cash does Cheney-Burton need to provide at the beginning of the first year in order to cover the $750 payments due over the five year period? ____________ 8b. If the payment required at the beginning of the third year was $190 thousand, would the binding constraint change? Provide numerical support for your answer. 8c. During which year will the first Government Security mature? ________ How many years does it take for the first Government Security to mature? ____________\ 8d. Should Cheney-Burton be willing to pay $6 thousand now to reduce the payment at the beginning of year four by $10 thousand? Provide numerical support for your answer. 8e. How much extra should Cheney-Burton be willing to pay now (the first year; 100,000 + ? - increases the amount the litigant gets now by how much) to reduce the beginning payment of year five from $200 (thousand) to $180 (thousand)?
6 OPTIMAL SOLUTION Objective Function Value = 652.451 Variable Value Reduced Costs -------------- --------------- ------------------ GS1 274.643 0.000 GS2 186.916 0.000 S1 90.893 0.000 S2 0.000 0.018 S3 154.206 0.000 S4 0.000 0.051 F 652.451 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 -1.000 2 0.000 -0.952 3 0.000 -0.889 4 0.000 -0.847 5 0.000 -0.759 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- GS1 -0.049 0.000 0.019 GS2 No Lower Limit 0.000 0.051 S1 -0.018 0.000 No Upper Limit S2 -0.018 0.000 No Upper Limit S3 -0.050 0.000 No Upper Limit S4 -0.051 0.000 No Upper Limit F 0.000 1.000 No Upper Limit RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 -552.451 100.000 No Upper Limit 2 29.563 125.000 No Upper Limit 3 -141.121 150.000 183.059 4

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