Question

Two models P and Q of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is .

• A. 15

Answer 1

The correct option is A 15
$\text{Max. Z = 100 × P + 80 × Q}$



$\text{Subjected to:}$

$5P+3Q\le 150$

$P+Q\le 40$

$\frac{P}{30}+\frac{Q}{50}=1$

$\frac{P}{40}+\frac{Q}{40}=1$

$\text{Putting value of corner point in objective function}$

$\text{Z(A) = 3200}$

$\text{Z(B) = 3500}$

$\text{Z(C) = 3000}$

$\text{Maximum at B,}$

$\text{P = 15, Q = 25}$

$\text{Hence the number of units of P to be produced is 15.}$