the profit for producing and selling a certain number, $n$, of goods is given by the function…

the profit for producing and selling a certain number, $n$, of goods is given by the function $p(n)=-25n^{2}+375n + 850$. at the break - even point, the profit is zero (i.e., $p(n)=0$). find the number of goods, $n$, that must be produced and sold to reach the break - even point.

the profit for producing and selling a certain number, $n$, of goods is given by the function $p(n)=-25n^{2}+375n + 850$. at the break - even point, the profit is zero (i.e., $p(n)=0$). find the number of goods, $n$, that must be produced and sold to reach the break - even point.

Answer

Explanation:

Step1: Set profit function to 0

$-25n^{2}+375n + 850=0$

Step2: Divide by -25

$n^{2}-15n - 34 = 0$

Step3: Factor the quadratic equation

$(n - 17)(n+ 2)=0$

Step4: Solve for n

$n - 17=0$ gives $n = 17$; $n+2=0$ gives $n=-2$. Since the number of goods $n$ cannot be negative, we discard $n=-2$.

Answer:

$17$