Question 650287: A company sells running shoes to dealers at a rate of $30 per pair if fewer than 65 pairs are ordered. If a dealer orders 65 or more pairs (up to 600), the price per pair is reduced at a rate of 4 cents times the number ordered. What size order will produce the maximum amount of money for the company?
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website! A company sells running shoes to dealers at a rate of $30 per pair if fewer than 65 pairs are ordered. If a dealer orders 65 or more pairs (up to 600), the price per pair is reduced at a rate of 4 cents times the number ordered. What size order will produce the maximum amount of money for the company?
Let amount of pairs of shoes to be sold, be x, and revenue, R(x)
Then: R(x) = 30x, if r < 65
R(x) = x(30 - .04x), or  , if 65 ≤ x ≤ 600
Maximum amount of shoes it needs to sell to realize maximum revenue:  , or  , or x = 375 pairs
With maximum amount of pairs to be sold to realize maximum revenue being 375, maximum revenue will occur at:
R(375) = 11,250 – 5,625
R(375), or maximum revenue for 375 pairs being sold = $
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