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.
Answers
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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