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  • A factory manufactures two types of screws, A and B. Assuming that he can sell all the screws he manufactures how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the ma

5. A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit. 

Answers (1)

best_answer

Let factory manufactures screws of type A and factory manufactures screws of type B. Thus, x\geq 0,y\geq 0.

The given information can be represented in the table as :

  screw A   screw B   availability
Automatic machine   4     6     4\times 60=240
hand operated machine     6      3      4\times 60=240
       

 Profit on a package of screw A  is Rs.7 and on the package of screw B  is 10.

Therefore, the constraint is  

                4x+6y\leq 240

               6x+3y\leq 240

                x\geq 0,y\geq 0

                 Z= 7x+10y

The feasible  region determined by constraints is as follows:

    

The corner points of the feasible region are  A(40,0),B(30,20),C(0,40),D(0,0)

The value of Z at corner points is as shown :

Corner points

Z= 7x+10y

  
A(40,0)                    280  
B(30,20)                    410 maximum
C(0,40)                     400  
D(0,0)                     0  

 The maximum value of z is 410 at B(30,20).

Thus, 30 packages of screw A  and 20 packages of screw B should be manufactured every day to get maximum profit.

Posted by

seema garhwal

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