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  • A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

4.  A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Types of toys Machines
I II III
A 12 18 6
B 6 0 9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

Answers (1)

best_answer

Let x and y toys of type A and type B.

The mathematical formulation of the given problem is as follows:

Minimize : z=7.5x+5y

Subject to constraint,

 2x+y\leq 60

 x\leq 20

 2x+3y \leq 120

  x,y\geq 0

The feasible  region determined by constraints is as follows:

       

The corner points of feasible region are A(20,0),B(20,20),C(15,30),D(0,40)

The value of Z at corner points is as shown :

 corner points 

z=7.5x+5y

  
   A(20,0)             150  

B(20,20)

             250  
  C (15,30)             262.5 maximum
   D(0,40)             200  

Therefore 262.5  may or may not be the maximum value of Z.

Hence, Z has maximum value of 262.5  at  point  C (15,30)

Posted by

seema garhwal

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