Question

A firm makes two products A and B. It 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 ti another company. Each tonne of A requires 20 machine hours of production time abd each tonne of B requires 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 $80 per tonne of A and $120 per tonne of B. To formulate the problem of maximising the profit as an LPP and to solve it graphically.

Answer 1

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

$x + y \le9$

$x\ge2, y\ge3$

Each tonne of A requires 20 machine 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:

$20x+50y\le360$

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:

$Z=80x+120y$ - maximize

$x + y \le9$

$20x+50y\le360$

$x\ge2, y\ge3$

solving for x and y we get x = 3, y = 6

Thus $Z=80x+120y=80\cdot3+120\cdot6=960$