Question

A merchant sells two models X and Y of TV at 25000 and50000 per set respectively.He gets a profit of *1500 on model X and 2000 on model Y. The sales cannot exceed20 sets in a month. If he cannot invest more than 6 lakh rupees, formulate the problem ofdetermining the number of sets of each type he must keep in stock for maximum profit.​

Answer 1

Given : A merchant sells two models X and Y of TV at 25000 and50000 per set respectively. He gets a profit of *1500 on model X and 2000 on model Y. The sales cannot exceed20 sets in a month.   he cannot invest more than 6 lakh rupees,

To Find :  formulate the problem of determining the number of sets of each type he must keep in stock for maximum profit.​

Solution:

Model X  SP = 25000

Model X  Profit    = 1500

Model X  CP  = 25000 - 1500 = 23500

Model Y  SP =  50000

Model Y  Profit    = 2000

Model Y  CP  =  50000 - 2000 = 48000

X , Y ≥ 0

X + Y ≤ 20

23500X  + 48000Y ≤ 600000

=> 235X  + 480Y ≤ 6000

=> 47X  +96Y ≤ 1200

47X  +96Y ≤ 1200

X + Y ≤ 20

Profit = 1500X  + 2000Y

X     Y     Profit

0     12      24000

1       12     25500

14     5       31000

15     5       32500

16     4       32000

20    0       30000

15 - X

5 - Y

for Maximum profit  = 32500

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