Question

Khadija and associates produces two products X and Y. Each unit of product X requires two kg of raw material and four labour hours for processing whereas each unit of product Y requires 3kg of raw materials and 3 labour hours, of the same type. Every week, the firm has an availability of 72 kg of raw materials and 108 labour hours. One unit of product sold yields sh. 50 and one unit of product gives sh 40 as profit. Formulate this promblem as linear programming promblem to determine as how many units of each products should be produced per week so that the firm can earn maximum profit. Assume that there is no marketing constraint so that all that is produced can be sold​

Answer 1

Explanation:

x = number of units of product X to be produced per week

y = number of units of product Y to be produced per week

The objective is to maximize the profit, which is given by:

Profit = 50x + 40y

The constraints are:

Raw material constraint: 2x + 3y ≤ 72

Labour constraint: 4x + 3y ≤ 108

Non-negativity constraint: x, y ≥ 0

Therefore, the linear programming problem can be formulated as

Profit = 50x + 40y

2x + 3y ≤ 72

4x + 3y ≤ 108

x, y ≥ 0

This problem can be solved using a graphical method or any standard optimization software. The solution will provide the optimal number of units of product X and Y that should be produced per week to maximize the profit.