Factory makes tennis rackets and cricket bats. A tennis basket 1.5 hours of a machine time and 3 hours of maching time and 1 hour of craftman’s tome. In a day, the factory has the availability of not more than 42 hour sof machine time and 24 hours of craftman’s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity.
(ii) If profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit to the factory when
Verified Answer
Let the no. of rackets manufactures be = x
Let the no. of cricket bats be = y+
Constraints, x ≥ 0; y ≥ 0
1.5x + 3y ≤ 42 ⇒ 3x + 6y ≤ 84 ≤ x + 2y ≤ 28
3x + y ≤ 24
(i) On plotting, the point of intersection of two eq. will give us the optimum no. of rackets and bats,
x = 4, y = 12
(ii) Z = 20x + 10y
common staded region OABC
Z(0,0)=0Z(0,14)=Rs140Z(8,0)=Rs160
Z(4, 12) = 80 + 120 = Rs 200
Max. Profit = Rs 200