P. Maria SheebaPG Student,

Mepco Schlenk Engineering College

1. A company makes 2 kinds of leather belts. Belt A is a high quality belt, and belt B is of lower quality. The respective profits are Rs.4.00 & Rs.3.00 per belt. Each belt of type A requires twice as much time as a belt of type B the company could make 1000 belts per day. The supply of leather is sufficient for only 800 belts per day (both A and B combined). Belt A requires a fancy buckle and only 400 buckles per day are available. There are only 700 buckles a day available for belt B. Determine the optimal product mix.

Given data:

A B

Profit per belt (in Rs.)

4 3

Production rate 2 1 1000(belts per day)

Leather Supply constraint

1 1 800(per day)

Availability of buckles(per day)

400 700

1. Key decision:No of belts produced in each type per day.

2. Decision Variables:x – no of belts of type A produced per day.y – no of belts of type B produced per day.

3. Feasible alternatives:x ≥ 0y ≥ 0

4. Constraints:2x + y ≤ 1000 (Production rate)x + y ≤ 800 (Leather availability)x ≤ 400 (Buckle availability)y ≤ 700 (Buckle availability)

5. Objective: Maximize the profit.z = 4x + 3y.

Mathematical Formulation