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Once upon a time, there was a
wicked Math Prof who loved to write word problems... |
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(#5 Pg 260 underlined number changed) COMPUTER WORLD is currently selling the
DVD-copier X-COPY for $40 per box,
and at that price has been selling 50 boxes per month. The store plans to
change the price, and estimates that for each $1 increase in price,
5 fewer boxes will be sold each month.
If the manufacturer charges COMPUTER WORLD $25 for each box of
X-COPY, at what selling price
x will COMPUTER WORLD maximize its profit P on all boxes of
X-COPY sold? |
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(3 points) For the problem in the box above, complete the equation which expresses
the relationship between x and P (show work: one number given as a reality check).
[Note : x = "selling price of one box of
X-COPY " :
you must not change this definition of x] |
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In the space below, differentiate the above P twice and find
any CVs of P (for one point). Finally (for one more point) name
the value of x at which P is largest. |
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Thus, P is biggest when x = |
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