Answer to Question #179623 in Operations Research for Laxmi deep

Question

A firm makes items A and B and the total number of items it can make in a day is 24 It takes one hour to make an item of A and only half an hour to make an item of B. The maximum time available per day is 16 hours. The profit on an item of A is Rs. 300 and on one item of B is Rs.

Answer 1

Let item A = x units

Let item B = y units

$x+y\le 24$

and,

$x+\dfrac{y}{2}\le16$

Profit, $Z = 300x+160y$

From the graph, we have points

$P(0,24) = 0+ 160\times 24 = 3840$

$Q(8,16) = 300\times16 + 0 = 4800$

$R(16,0) = 300\times 8 + 16\times160 = 4960$

$S(0,0) = 0$

$Q(8,16)$ will maximise the profit.