Question

2. (a) A firm makes two products A and B has a total production capacity of 9 tonnes per

day, with A and B utilizing the same production facilities. The firm has a

permanent contract to supply at least 2 tonnes of A per day to another company.

Each tone of A requires 20 machine hours of production time and each tone 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 Rs.

80 per tonne of A and Rs. 120 per tonne of B. Formulate the problem of maximising

the profit as an LPP and solve it graphically.

Answer 1

Let product A be x and product B be y. Hence we have

$x+y\le9$

$x\ge2 , y\ge 3$

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

$20x+50y\le 360$

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,

Maximize : $Z = 80x+120y$

Solving for x and y from the above equations

We get,

$x=3, y=6$

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

Graphically it can be represented as