LINEAR PROGRAMMING FORMULATION PROBLEMS SET 3

CURRENCY ARBITRAGE MODEL.

Suppose that a company has 5 million US $ that can be exchanged for various international currencies. Currency dealers have set the following restrictions on the amount of any single transaction : 5 million US$, 3 million euros, 3.5 million pounds, 100 million yen and 2.8Million Kuwaiti Dinars.The typical exchange rates existing at present are given below.

$ € ₤ ¥ KD

$ 1 .769 .625 105 .342

€ 1 .813 137 .445

₤ 1 169 .543

¥ 1 .0032

KD 1

Is it possible to increase the dollar holdings by circulating currencies in the market?

INVESTMENT DECISION MODEL

An investment counselor is attempting to determine the best investment mix for one of his clients. Some information about the possible options are given in the table below.

SHARES UNDER CONSIDERATION

A B C D E FCurrent price per share 80 100 160 120 150 200

Projected annual growth rate 8% 7% 10% 12% 9% 15%

Projected annual dividend per share Rs 4 4.5 7.5 5.5 5.75 0

Projected risk in return 5% 3% 10% 20% 6% 8%

Client wants to invest 50 lakhs of Rs. with the following conditions.i) investment in F not to be more than Rs5L. ii) Maximum investment in A and B put together not to exceed Rs10 Lakhs. iii) Total weighted risk to be less than 10%

iv) At least 100 shares of each should be held. v) Investment in A and B must be at least 10% of total investment.v) Dividends for the year should be at least Rs 30000.

If the objective is to maximize the rupee rate of return for one year, formulate an LPP to help theCounselor.

MULTI PERIOD PRODUCTION-INVENTORY MODEL.

Acme manufacturing company has contracted to deliver home windows over the next 6 months.The demands for each month are 100,250,190,140,220 and110 units respectively. Production cost per window varies from month to month depending on the cost of labour,material and utilities. Acme estimates the same to be Rs 500,450,550,480,520 and 500 over the next six months. Totake advantage of these fluctuations, Acme may elect to produce more in a month than the demand and hold the excess units for delivery in the later months.This however will result in an additional storage cost of Rs 80 per unit per month. Formulate an LPP to get the optimumproduction schedule.

MULTI PERIOD PRODUCTION SMOOTHING MODEL.

A Company plans to manufacture a product for the next 4 months, the demands for the same being 520,720,520 and 620 respectively. The company has 10 permanent workers, but can meet fluctuating requirements by hiring and firing temporary workers. The costs of hiring and firing are Rs.200 and 400 per worker respectively. A permanent worker produces 12 units per month, while a temporary worker can produce only 10 units. The cost of holding extra stocks is Rs 50 per unit per month. Develop an optimal hiring/firing policy for the company over the next 4 months.

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