Question

A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only. The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively.

For maximization of profits, the daily production quantities of P and Q toys should respectively be

• A. 800, 600
• B. 500, 1000
• C. 1000, 1000
• D. 1000, 500

Answer 1

The correct option is D 1000, 500

$\text{Given data:}$

$P+2Q\le 2000...\left(i\right)$

$P+Q\le 1500...\left(ii\right)$

$Q\le 600...\left(iii\right)$

$\text{Objective function}$

$z_{max}=3P+5Q$



$\text{At point A, z = 3 × 800 + 600 × 5 = 5400}$

$\text{At point B, z = 3 × 1000 + 5 × 500 = 5500}$

$\text{At point C, z = 3 × 1500 + 5 × 0 = 4500}$

$\text{At point D, z = 3 × 0 + 5 × 600 = 3000}$

$\text{Hence z to be maximum at B(1000, 500)}$