Question

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

1.3 million hoops
1.4 million hoops
15 million hoops
30 million hoops

Answer 1

The company previously produced approximately 1.4 million basketball hoops to make the same profit.

Step-by-step explanation:

In order to find out how many basketball hoops the company previously produced to make the same profit, we can set up an equation using the given information.

The profit is calculated by subtracting the total cost from the total revenue. We know that the profit is $15 million and the cost to make each hoop is $30. Let's denote the number of hoops previously produced as x.

The equation is: $15 million = ($50 - 5x^2 - $30x).

Simplifying the equation gives us the quadratic equation: 5x^2 + $30x - $35 million = 0.

We can now solve this quadratic equation to find the value of x using the quadratic formula or factoring.

After solving the equation, we find that x is approximately 1.4 million hoops. Therefore, the company previously produced approximately 1.4 million basketball hoops to make the same profit.