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Question
A company produces two types of products say type A and B. Profits on the two types of product are ₹ 30/- and ₹ 40/- per kg respectively. The data on resources required and availability of resources are given below.
| Requirements | Capacity available per month | ||
| Product A | Product B | ||
| Raw material (kgs) | 60 | 120 | 12000 |
| Machining hours/piece | 8 | 5 | 600 |
| Assembling (man hours) | 3 | 4 | 500 |
Formulate this problem as a linear programming problem to maximize the profit.
Solution
(i) Variables: Let x1 and x2 denote the two types products A and B respectively.
(ii) Objective function:
Profit on x1 units of type A product = 30x1
Profit on x2 units of type B product = 40x2
Total profit = 30x1 + 40x2
Let Z = 30x1 + 40x2, which is the objective function.
Since the profit is to be maximized, we have to maximize Z = 30x1 + 40x2
(iii) Constraints:
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
(iv) Non-negative constraints: Since the number of products on type A and type B are non-negative, we have x1, x2 ≥ 0
Thus, the mathematical formulation of the LPP is Maximize Z = 30x1 + 40x2
Subject to the constraints,
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
x1, x2 ≥ 0
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