# math

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a clothing manufacturer has 100m of silk and 180 m of wool. to make a suit requires 2m of silk and 3m of wool and to make a dress requires 1m of silk and 2m of wool. if the profit on a suit is 108\$ and the profit on a dress is 60\$ how many suits and dresses should be made to maximize profit?

This looks like a problem in 'linear programming'

let s represent the number of suits and d the number of dresses.

then 2s + d <= 100 and 3s + 2d <= 180
a d vs
graph these two inequations with s and d as the axes forming a polygon with the s and d axes.

Now consider the equation Profit = 108s + 60d

Shift this equation away from the origin into the first quadrant, until the line p=108s+60d reaches the farthest vertex from the origin of your polygon.

Your polygon only has one vertex in the interior region of the first quadrant, I think it is s=20 and d=30 for a maximum profit of \$3960

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