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Question

A dealer wishes to purchase toys A and B. He has Rs. 580 and has space to store 40 items. A costs Rs. 75 and B costs Rs. 90. He can make profit of Rs. 10 and Rs.15 by selling A and B respectively assuming that he can sell all the items that he can buy formulation of this as L.P.P. is

A
Maximize z=10x+15y
Subject to x+y40,75x+90y580,x0,y0
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B
Maximize z=10x+15y
Subject to x+y40,x0,y0,75x+90y580
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C
Maximize z=15x+10y
Subject to x+y40,75x+90y580,x0,y0
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D
Maximize z=10x+15y
Subject to x+y40,75x+90y580,x0,y0
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Solution

The correct option is A Maximize z=10x+15y
Subject to x+y40,75x+90y580,x0,y0
Let the dealer have x items of A and y items of B.
Clearly, x0,y0
The total number of items must not exceed 40, and so x+y40
Also, since he has only Rs.580 with him, the total cost must not exceed that.
75x+90y580
Since we need to maximize the profit, which can be written as z=10x+15ysince by selling 1 item of A, the profit earned is Rs. 10 and Rs. 15 for B.

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