question_answer 1)

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 craftman’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 maximum profit of the factory when it works at full capacity.  

Answer:

Let number of rackets made = x       and number of bats made = y       The number of hours for making one unit of each item is given below :

Item	Machine time	Craftman?s time
Racket	1.5	3
Bat	3	1
Time available	42 hrs	24 hrs

      Therefore the above L.P.P. is given as       (i) Maximize, Z = x + y, subject to the constrains             1.5x + 3y  3x + y       i.e.  0.5x + y       i.e.  x + 2y m 3x + y       L1 : x  +2y = 28                    L2 : 3x + y = 24                                                           Here Z is maximum at E(4, 12)                Number of Rackets = 4       Number of Bats = 12       (ii) Profit function is, P = 20x + 10y       Profit is maximum at x = 4 and y = 12.        P = 20 × 4 + 10 × 12       = 80 + 120 = Rs.200.                  Maximum Profit = Rs.200.