anufacturers produce tow products A and B each of which gives a net profit of birr 4 and 3 respectively per unit. These are made either in plant I or plan II. Plant I and II have capacities of 72 and 48 hrs a day. Plant I take 2hrs and 1hr to produce A and B respectively. The corresponding figures of plant II are 1 and 2hrs. Formulate linear programming model.

Question

anufacturers produce tow products A and B each of which gives a net profit of birr 4 and 3 respectively per unit. These are made either in plant I or plan II. Plant I and II have capacities of 72 and 48 hrs a day. Plant I take 2hrs and 1hr to produce A and B respectively. The corresponding figures of plant II are 1 and 2hrs. Formulate linear programming model.

Answer 1

Let:

x1 = number of units of product A produced in plant I
x2 = number of units of product A produced in plant II
y1 = number of units of product B produced in plant I
y2 = number of units of product B produced in plant II

Objective function:
Maximize profit = 4x1 + 4x2 + 3y1 + 3y2

Constraints:
1. Plant I's capacity constraint:
2x1 + y1 ≤ 72

2. Plant II's capacity constraint:
x2 + 2y2 ≤ 48

3. Non-negativity constraint:
x1, x2, y1, y2 ≥ 0

This linear programming model will help optimize the production of products A and B in plants I and II to maximize the total profit subject to the capacity constraints of both plants.