Question

A company needs 50 new machines. The machines have an economic life of two years

and can be purchased for Rs 4,500 or be leased for Rs 2,800 per year. The purchased

machines, at the end of two years, have no salvage value. Company has Rs 1,00,000

in uncommitted funds that can be used for the purchase or the lease of machines at

the beginning of year 1. The company can obtain a loan of upto Rs 2,00,000 at 18 per

cent interest per year. According to the terms of loans, the company has to repay the

amount borrowed plus the interest at the end of each year. Each machine can earn

Rs 3,000 per year. The earnings from the first year can be used to lease costs and the

repayment of debt at the start of the second year. The company wants to minimize the

total cost of using 50 machines over a two-year period. The objective is to minimize

the costs of purchasing machines or leasing machines during the years 1 and 2, and to

minimize the interest payments on funds borrowed to obtain the machines. Formulate

this problem as a linear programming problem.​

Answer 1

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