Question

Suppose that a when a cell phone store charges 16$ for a car charger, it sells 92 units. When it drops the price to 15$ it sells 96 units. Assume that demand is a linear function of price.
If each phone charger costs 1$ to make, what price should the store charge to maximize its profit?
If x is the number of times the price is reduced by one dollar.

Find a function for total profit with respect to x. A negative value for x will mean the price is increased. ...?

Answer 1

If you put the dollar decrease as x, you sell charge
16−x
dollars and sell
92+4x
units for a profit of
(16−x)(92+4x)−(2+4x)
dollars. the last subtraction because your cost is $1 per unit multiply out and
get
P=−4x2−32x+1470
which will have a maximum at the vertex
x=−b/2a

= 32/(2(−4)) 

= −4

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