Answer to Question #185199 in Operations Research for Vaishu

Question

A firm makes two products A and B has a total production capacity of 9 tonnes per day , with A and B utilising the same production facilities . The firm has a permanent contract to supply at least 2 tonnes of A per day to another company. Each tonne of A requires 20 machine hours of production time and each tonne of B required 50 machine hours of production time . The daily maximum possible number of machine hours is 360 . All the firm's output can be sold and the profit made is Rs. 80 per tonne of A and Rs. 120 per tonne of B . Formulate the problem of maximizing the profit as an LPP and solve it graphically

Answer 1

Let the product A be x and product B be y. Therefore we have :

$x+y \le 9$

$x \ge2, y \ge 3$

Each tonne of A requires 20 machines hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360, thus

$20x+ 50y \le 360$

All the firm's output can be sold and the profit made is 80$ per tonne of A and 120$ per tonne of B. Thus,

Max $Z = 80x+120y$

$x+y \le 9$

$20x+ 50y \le 360$

$x \ge2, y \ge 3$

Solving for x and y we get $x=3$ and $y =6$

Thus, $Z = 80(3) + 120(6) = 960$

Graphically it can be solved as :