The monthly revenue R achieved by selling x wristwatches is figured to be R(x)=8

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The monthly revenue R achieved by selling x wristwatches is figured to be R(x)=85x-0.2x^2. The monthly cost C of selling x wristwatches is C(x)=32x+1850. 

A. How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?

B. Profit is given as P(x)=R(x)-C(x). What is the profit function? 

C. How many wristwatches must the firm sell to maximize profit? What is the maximum profit?

Oct 12th, 2015

Hello!

For the quadratic function ax^2 + bx + c where a<0 the point of maximum is x0=-b/(2a).

A) here a = -0.2, b = 85, x0 = -b/(2a) = 85/0.4 = 212.5.
Because the number of wristwatches must be integer, there are two possibilities: 212 and 213.
For both variants R(x)=9031.2  (R(212.5) = 9031.25).

B) P(x) = R(x) - C(x) = 85x - 0.2x^2 - 32x - 1850 = -0.2x^2 + 53x - 1850.

C) here a = -0.2, b = 53, x0 = -b/2a = 53/0.4 = 132.5
Also consider 132 and 133, for these x'es P(x) = 1661.2.
(P(x0) = 1661.25).

Please ask if something is unclear.
Oct 12th, 2015

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Oct 12th, 2015
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Oct 12th, 2015
Sep 23rd, 2017
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