Question

A manufacturer of sports goods can produce as many as 60 hockey sticks and as many as 45 cricket bats per day.It takes 3 hour of labour to produce one hockey stick and 4 hour of labour to produce one cricket bat.The company has upto 240 hour of labour available for production each day.If the profit is Rs12 on each hockey stick and rs 18 on each bat , find the number of units of each item the firm should produce to gain the maximum profit each day.​

Answer 1

Let,

x be the number of hockey sticks.

y be the number of cricket bats.

Given,

Daily profit on hockey stick = 12 x

Daily profit on cricket bats = 18 y

Total profit = 12 x + 18 y

We know the total number of cricket bats and hockey is non negative.

x ≥ 0

y ≥ 0  

Given,

60 hockey sticks produced each day,

x ≤ 60  

45 cricket bats produced each day,

y ≤ 45

The objective is to maximise the profit., therefore the objective function is 12 x + 18 y

The LP problem :

Maximise :  

Z =12 x + 18 y

Constraints :

3 x + 4 y ≤ 240                          (up to 240 h labour is available)

x ≤ 60   ;   y ≤ 45

x ≥ 0  ; y ≥ 0