# HOMEWORK 8.pdf - HOMEWORK 8 INTEGER LP BINARY VARIABLES...

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HOMEWORK # 8: INTEGER LP. BINARY VARIABLES Exercise 1. The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck. The company has recently contracted to supply gasoline distributors in southern Ohio, and it has a \$800,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of gasoline tank trucks are available. Capacity Purchase Monthly Truck Model (gallons) cost Op. costs Super tanker 5,000 \$67,000 \$550 Regular Line 2,500 \$55,000 \$425 Econo-Tanker 1,000 \$46,000 \$350 The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline. Because of the size and speed difference of the trucks, the number of deliveries or round trips possible per month for each truck model will vary. Trip capacities are estimated at 15 trips per month for the Super Tanker, 20 trips per month for the Regular Line, and 25 trips per month for the Econo-Tanker. Based on maintenance and driver availability, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company has decided to purchase at least three of the new Econo-Tankers for use on short-run, low demand routes. As a final constraint, the company does not want more than half the new models to be Super-Tankers. a. Formulate a mathematical model to solve the problem assuming that the company wishes to satisfy the gasoline demand with a minimum monthly operating cost. b. Solve the problem in EXCEL. c. Suppose that the demand was 480,000 gallons instead. Change the EXCEL values to find the new solution. Note that, if you got the right answer, the number of ST and RL required to minimize the operation costs is not an integer amount. Try to use rounding to find the best feasible solution. Which of the four alternatives (round up/down each of the two non-integer solutions) are feasible? Which is the best? d. Use EXCEL to find the optimal integer solution. Discuss this new solution. Exercise 2. Spencer Enterprises is attempting to choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next 3 years are summarized as follows: 1