SOLUTION: Suppose that the price per unit in dollars of a cell phone production is modeled by p=$45-0.0125x, where x is in thousands of phones produced, and the revenue represented by thousa

Question 1176178: Suppose that the price per unit in dollars of a cell phone production is modeled by p=$45-0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R=x•p. Find the production level that will maximize revenue.
Answer by ikleyn(52772) (Show Source): You can put this solution on YOUR website!
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The revenue is 


    R(x) = x*(45-0.0125x) dollars.


This formula represents  a quadratic function, whose plot is a parabola opened downward.


It gets the maximum at the value of x which is exactly midway between the x-intersections.


The x-intersections are  x= 0  and  x=  = 3200,

so the maximum of the function is at  x= 1600,


To get the value of the maximum, substitute  x= 1600 into the Revenue formula


     = 1600*(45-0.0125*1600) = 40,000 thousand dollars.    ANSWER

Solved.

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