Linear programming is used to optimize allocation of constrained resources to maximize objectives like profit, sales or costs. It involves determining the optimal production quantities of two products, A and B, given constraints on raw materials and labor hours, to maximize total profit. The marketing department of Everest company collected data on advertising mediums, reach, costs and constraints to determine the optimal allocation of their Rs. 70,000 budget across mediums to cover at least 40,000 families while adhering to constraints.

1. Linear programming

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. • 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. • 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. Medium No of families Cost per ad Max Expected
covered (Rs) availability (no exposure
of times)
TV (30sec) 3000 8000 8 80
Radio (15 sec) 7000 3000 30 20
Sunday edition 5000 4000 4 50
Magazine 2000 3000 2 60