a factory producing clothes.the available material are 750m^2 of cotton and 1000m^2 of polyester.a pair of sweatpant need 1 m^2 cotton and 2m^2 polyester.one sweat short need 1m^2 cotton and 1m2 polyester.price of sweatpants is $50 and price of sweatshirt is $40.how much type of clothes made in order to profit to be maximized??
Answers
Given : A factory is producing clothes the available materials are 750m^(2) of cotton and 1000m^(2) of polyester.
A pair of sweatpants needs 1m^(2) of cotton and 2m^(2) of polyester
One sweatshirt needs 1.5m^(2) of cotton and 1m^(2) of polyester
The price of the sweatpants is $50 and the price of the sweatshirt is $40
To Find : How much of each type of clothes should be made in order for the profit to be maximized?
Solution:
sweatpants = P
sweatshirt = S
P, S ≥ 0
P + 1.5S ≤ 750
=> 2P + 3S ≤ 1500
2P + S < 1000
Profit Z = 50P + 40S
P S Profit Z = 50P + 40S
0 500 20000
375 250 28750
500 0 25000
28750 is maximum
Maximum profit is sweatpants = 375 and sweatshirts = 250
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