Question

A computer software company models its profit with the function P(x) = -x2 + 15x – 34 where x is the number of games, in hundreds, that the company sells and P(x) is the profit, in thousands of dollars. How many games must the company sell to get $16,000 in profit?

Answer 1

Explanation:

A computer software company models its profit with the function :

`P(x) = x^2 + 15x -34` ....(1)

Where

x is the number of games, in hundreds, that the company sells and P(x) is the profit, in thousands of dollars.

We need to find the number of games the company sell to get $16,000 in profit.

Put P(x) = 16,000 in equation (1).

`x^2 + 15x -34=16000\\\\x^2+15x-34-16000=0\\\\x^2+15x-34-16000=0\\\\x^2+15x-16034=0`

Using quadratic formula with a=1, b=15, c=-16034.

`x=\frac{-15+\sqrt{15^(2)-4\left(1\right)\left(-16034\right)}}{2\left(-1\right)}, \frac{-15-\sqrt{15^(2)-4\left(1\right)\left(-16034\right)}}{2\left(-1\right)}\\\\=-119.34, 134.34`

Neglecting negative value,

No of games = 134 (approx)