A company produces two types of leather belts, say a and
b. Belt a is superior quality and b is inferior. Profit on the two are 40p and 30p per belt, respectively. Each belt of type a requires twice as much time as required by a belt of type
b. If all the belts were of type b, the company could produce 1000 belts per day. But supply of leather is sufficient only' for 800 belts per day. Belt a requires a fancy buckle and only 4000 of them are available per day. For belt b only 700 buckles are available per day. How should the company manufacture the two types of belts in order to have a maximum overall profit ?
Answers
Given : A company produces two types of leather belts, say a and
b. Belt a is superior quality and b is inferior. Profit on the two are 40p and 30p per belt, respectively. Each belt of type a requires twice as much time as required by a belt of type b. If all the belts were of type b, the company could produce 1000 belts per day. But supply of leather is sufficient only' for 800 belts per day. Belt a requires a fancy buckle and only 400 of them are available per day. For belt b only 700 buckles are available per day.
To Find : How should the company manufacture the two types of belts in order to have a maximum overall profit
Solution:
company could produce 1000 belts per day of b type
Total Time available = 1000t
t is time taken to produce belt b
2t is time taken to produce belt a
a(2t) + b(t) ≤ 1000t
=> 2a + b ≤ 1000
a + b ≤ 800
a ≤ 400
b ≤ 700
Profit = 40a + 30b
a b Profit = 40*a + 30b
0 700 21000
100 700 25000
200 600 26000
400 200 22000
400 0 16000
Belt a = 200
Bent b = 600
to have a maximum overall profit
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