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# Linear programming

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### Linear programming

1. 1. Linear programming
2. 2. • A large number of decisions involve allocation of resources which are subject to constraints with the objective of optimizing profit/sales/costs• Linear programming is about optimizing a certain function, subject to a set of constraints
3. 3. • A firm is engaged in producing two products A and B. Each unit of A requires 2 kg of raw material and 4 labor hours for processing and each unit of B requires 3 kg of raw material and 3 hours of labor. Every week the firm has an availability of 60 kg of raw material and 96 labor hours. One unit of A sold yields a profit of Rs 40.00 and one unit of B sold yields a profit of Rs 35.00• Formulate the problem as a liner programming problem to determine how many units of each product should be produced to maximize profit.
4. 4. • The marketing department of Everest company hs collected information on the problem of advertising for its products. This relates to advertising media available, the number of families expected to be reached with each alternative, cost per advt., the maximum availability of each medium and the expected exposure of each.• The advertising budget is Rs 70,000.• Atleast 40000 families should be covered• At least 2 insertions be given in the Sunday edition, but not more than 4 advts to be given on TV
5. 5. Medium No of families Cost per ad Max Expected covered (Rs) availability (no exposure of times)TV (30sec) 3000 8000 8 80Radio (15 sec) 7000 3000 30 20Sunday edition 5000 4000 4 50Magazine 2000 3000 2 60