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  • A toy company manufactures two types of dolls, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B.

10.A toy company manufactures two types of dolls, A and B. Market research and available resources have  indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12  and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

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Let  x and y be number of dolls of type A abd B respectively that are produced per week.

Mathematical formulation of given problem is as  follows:

Maximize : z=12x+16y

Subject to constraint ,

                           x+y\leq 1200

                           y\leq \frac{x}{2}\Rightarrow x\geq 2y

                         x-3y\leq 600

                            x,y\geq 0

The feasible  region determined by constraints is as follows:

       

The corner points of feasible region are A(600,0),B(1050,150),C(800,400)

The value of Z at corner points is as shown :

 corner points 

z=12x+16y

  
   A(600,0)             7200  

B(1050,150)

             15000  
  C(800,400)              16000 Maximum
                 

Therefore 16000 is maximum value of Z .

Hence , Z has minimum value 16000 at  point  C(800,400)

Posted by

seema garhwal

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