Question

The price that a company charged for a basketball hoop is given by the equation 50-5x^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?

A) 1.3 million hoops B) 1.4 million hoops
C) 15 million hoops D) 30 million hoops

Answer 1

1.3 million

Explanation:

its right on edge

Answer 2

TR ( total revenue ) = P ( price ) x Q ( quantity ) = ( 50 - 5 x² ) · x
TR = 50 x - 5 x³
Profit = TR - TC ( total cost ) = 50 x - 5 x³ - 30 x = - 5 x³ + 20 x
If x = 1 ( 1 million hoops ):
15 = - 5 · 1³ + 20 · 1 = - 5 + 20
If we want to find another production that makes the same profit:
15 = - 5 x³ + 20 x
5 x³ - 20 x + 15 = 0 / : 5
x³ - 4 x + 3 = 0
( x - 1 ) ( x² + x - 3 ) = 0

`x_(12) = (-1+ √(1+12) )/(2)= (-1+ √(13) )/(2)`
x ≈ 1.3
Answer:
A ) 1.3 million hoops