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 I 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 maximum profit of the factory when it works at full capacity
hour of work on machine


question----->>somebody tell me that how can 1 day have 42 hours????​

Answer 1

Answer:

Let number of tennis racket be made is X and number of cricket bat be made is Y

Since, tennis bat requires 1.5 hours and cricket bat requires 3 hours of machine time. Also, there is maximum 42 hours of machine time available.

∴1.5X+3Y≤42

⇒X+2Y≤28 ...(1)

Since, tennis bat requires 3 hours and cricket bat requires 1 hours of craftmans time. Also, there is maximum 24 hours of craftmans time available.

∴3X+Y≤24 ...(2)

Since, count of an object can't be negative.

∴X≥0,Y≥0 ...(3)

We have to maximize profit of the factory.

Here, profit on tennis racket is 20 Rs and on cricket bat is 10 Rs

So, objective function is Z=20X+10Y

Plotting all the constraints given by equation (1), (2) and (3), we got the feasible region as shown in the image.

Corner points Value of Z=20X+10Y

A (0,14) 140

B (4,12) 200 (maximum)

C (8,0) 160

Hence,

(i) 4 tennis rackets and 12 cricket bats must be made so that factory will work at full capacity.

(ii) Maximum profit of factory will be 200 Rs