Question

Smith & Johnson produces a variety of men’s clothing. Their highest selling items are their fitted dress shirts. The profit earned from the sale of these shirts can be modeled by the expression -20x2+1,800x, where x is the price of one dress shirt. If p is the maximum profit earned from the sale of the dress shirts, write an equation that shows how the expression can be rewritten to model the price at which the shirts should be set in order to maximize profit.

Answer 1

P=x(-x+90)

Explanation:

Step one:

given

Price

`P= -20x^2+1800x`

where P is the maximum profit

x is the price of one shirt

Step two:

To rewrite the expression let us first divide through by 20

`P= (-20x^2)/(20) +(1800x )/(20)\\\\P=-x^2+90x`

Factoring x out we have

`P=-x^2+90x\\\\P=x(-x+90)`

Hence the rewritten expression equation for the price is

P=x(-x+90)