Question

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. 

(i) What number of rackets and bats must be made if the factory is to work at full capacity? 

(ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, find the maximuin profit of the factory when it works at full capacity.

Answer 1

Z = x +y 

P = 20x + 10 y 

Z subject to constraints

ABCD is the solution region 

A(0,0) Z = 0 P = 0

ABCD is the solution region 

A (0,0) Z = 0 P = 0 

B (8,0) Z = 8 P=20 x 8 = Rs. 160 

C (4. 12) Z = 16 P = Rs. 200 

D (0,14) Z = 14 P = Rs.140 

At C (4, 12) Z is maximised to 16 and then profit is also maximised by the manufacture of 4 rackets and 12 bats.