Question

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the

Answer 1

Time on	A(x)	B(y)	Total
(i) automatic machine	4min	6min	4hrs
(ii) Hand operated machine	6min	3min	4hrs
(iii) Profit	Rs 7	Rs10

P = 7x +10y

(i) 4x + 6y ≤ 240 ⇒ 2x + 3y ≤120 

(ii) 6x + 3y ≤ 240 ⇒ 2x + y ≤ 80 

(iii) x ≥ 0 ; y ≥ 0

ABCD is the solution region 

A (0,0) P = 7 x 0+10 x 0 = 0 

B (40, 0) P = 7 x 40+ 10 x 0 = 280 Rs. 

C (30, 20) P = 7 x 30+ 10 x 20 = 410 Rs. 

D (0, 40) P = 7 x 0+ 10 x 40 = 400 Rs 

At C (30,20)P is maximised 

∴ 30 types of screw A & 20 types of screw B.