Question 798189: A company sells running shoes to dealers at a rate of $34 per pair if fewer than 70 pairs are ordered. If a dealer orders 70 or more pairs (up to 600), the price per pair is reduced at a rate of 5 cents times the number ordered. What size order will produce the maximum amount of money for the company?
So far I have... $34 if x<70 and 70>or equal to -.05x < 600
thankyou
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If you need to show work, just write:
 so maximum at 
UNDERSTANDING THE PROBLEM:
The price per pair of running shoes is
$ if  or
$ if 
They must be sure their customers will not place large orders, because for an order of 600 pairs, the price per pair would be
$ = $ = $
Anyway, if the company sells  pairs, between 70 and 600 pairs (), they get
$
The amount (in $) they get, as a function of , is a quadratic function:
or
For this problem, that function is only defined for some values of , . (The domain of that function is restricted by ).
The function without restrictions graphs as a parabola,
a nicely symmetrical curve, with a maximum exactly halfway between the zeros,
which are at  ,
and where  <-->  <-->  <-->  .
So that maximum is at exactly  .
Easy. No memorized formulas required.
WHAT IS EXPECTED:
Your teacher may expect you to multiply to get from
to ,
and then apply memorized facts and formulas.
You've been taught the fact that a quadratic function 
has a maximum or minimum at  ,
which is a maximum if  , and is a minimum if  .
In this case  , so there is a maximum,
and calculates as 
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