SOLUTION: The senior class plans on selling clothing. The hats cost $5 apiece the t-shirts cost $9, and they have $2250 to spend purchasing the items. If their profit is $4 from each hat and

Question 1171320: The senior class plans on selling clothing. The hats cost $5 apiece the t-shirts cost $9, and they have $2250 to spend purchasing the items. If their profit is $4 from each hat and $5 from each t-shirt, how many hats and t-shirts should they purchase in order to maximize their profit?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The only constraint on the numbers of hats and t-shirts is the amount of money they have to spend buying the items. Common sense -- or a basic familiarity with the formal method of solving this kind of problem -- tells us that the maximum profit is either with only hats or with only t-shirts.

For $2250, the maximum number of hats they can buy is 2250/5 = 450; by selling 450 shirts their profit would be 450*$4 = $1800.

For $2250, the maximum number of t-shirts they can buy is 2250/9 = 250; by selling 250 t-shirts their profit would be 250*$5 =$1250.

ANSWER: the maximum profit is obtained by buy and sell only 450 hats.

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