Question

The price that a company charged for a basketball hoop is given by the equation 50-x^2 where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

Answer 1

Answer:

A.  1.3 million hoops

on edg

Answer 2

Answer: 2.125 million (Approx)

Step-by-step explanation:

Let the company initially produced x million hoops.

Therefore, after reducing 1 million hoops,

New number of hoops = (x-1)

Since, Profit = Sale price - Cost price

The cost price of 1 hoop = 30 dollars

Thus, the cost price of (x-1) million hoop = 30(x-1) dollars

According to the question,

The price that a company charged for a basketball hoop is given by the equation $50-(x-1)^2$

Thus the sales price of x million hoops = $50 - (x-1)^2$

Hence, the company's profit = $(50 - (x-1)^2) - 30(x-1)$

Again According to the question,

The company's profit = 15 million,

⇒ $(50 - (x-1)^2) - 30(x-1)=15$

⇒ $50-x^2-1+2x-30x+30=15$

⇒ $-x^2-28x+79-15=0$

⇒ $-x^2-28x+64=0$

⇒ $x^2+28x-64=0$

By solving this equations we get,

x = -2(7+√65) and x = 2(√65-7)

But, the number of hoops can not be negative,

Thus, the initial number of  hoops = 2(√65-7) million =2.1245154966 million ≈2.125 million