Question

The weekly profit of a company is modeled by the function w = –g2 + 120g – 28. The weekly profit, w, is dependent on the number of gizmos, g, sold. If the break-even point is when w = 0, how many gizmos must the company sell each week in order to break even?

Answer 1

Answer:

120 gizmos.

Explanation:

We have been given that the weekly profit of a company is modeled by the function $w =-g^2+120g-28$. The weekly profit, w, is dependent on the number of gizmos, g, sold. The break-even point is when  $w=0$.

To find the number of gizmos the company must sell each week in order to break even, we will substitute $w=0$ in profit function as:

$0 =-g^2+120g-28$

$-g^2+120g-28=0$

Now, we will use quadratic formula to solve for g.

$g=\frac{-120\pm\sqrt{120^2-4(-1)(-28)}}{2(-1)}$

$g=\frac{-120\pm\sqrt{14400-112}}{-2}$

$g=\frac{-120\pm\sqrt{14288}}{-2}$

$g=\frac{-120\pm 119.53242237987}{-2}$

$g=\frac{-120-119.53242237987}{-2}\text{ or }g=\frac{-120+119.53242237987}{-2}$

$g=\frac{-239.53242237987}{-2}\text{ or }g=\frac{-0.46757762013}{-2}$

$g=119.76621118\text{ or }g=0.2337888$

$g\approx 120\text{ or }g\approx 0.23$

We will take the larger value for the number of gizmos.

Therefore, the company must sell 120 gizmos each week in order to break even.