Question

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are

Standard form: - 2 p^2 + 24p - 54

Factored form: -2(p - 3)(y-9)

Vertex form: -2(p-6)^2 + 18.

Which form is most useful for finding a. The prices that give a profit of zero dollars?

b. The profit when the price is zero?

c. The price that gives the maximum profit?​

Answer 1

Explanation:

If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.

a). The prices that give a profit of zero dollars.

Expression that is most useful,

Factored form: -2(p - 3)(p - 9) = 0

p = 3, 9

b). The profit when the price is zero .

Standard form:

Profit = -2p² + 24p - 54 = 0

-p² + 12p - 27 = 0

-p² + 3p + 9p - 27 = 0

-p(p - 3) + 9(p -3) = 0

(-p + 9)(p - 3) = 0

p = 3, 9

c). The price that gives the maximum profit.

Vertex form: -2(p - 6)² + 18

Vertex of the given expression → (6, 18)

Maximum profit will be at p = 6.

Therefore, profit = -2(6 - 6)² + 18 = 18