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Unformatted text preview: NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA3252 Linear and Network Optimization Tutorial 1 1. A small bank is allocating a maximum of $30,000 for personal and car loans during the next month. The bank charges an annual interest rate of 14% for personal loans and 12% for car loans. Both types of loans are repaid at the end of a one-year period. The amount of car loans should be at least twice as much as that of personal loans. Past experience shows that about 3% of personal loans and 2% of car loans are never paid. Formulate the problem of determining the allocation of the funds to maximize the net return for the bank as a linear programming model. Solve the problem graphically. 2. A company produces and sells two different products. The demand for each prod- uct is unlimited but the company is constrained by cash availability and machine capacity. Each unit of the first and second product need 3 and 4 machine hours respectively. There are 20,000 machine hours available in the current productionrespectively....
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- Spring '10