suppose that the fixed cost for a product is $455 and the break - even quantity is 65. find the marginal…

Explanation:

Step1: Recall break - even formula

At break - even, profit $P = 0$. The profit function is of the form $P(x)=mx + b$, where $m$ is the marginal profit (slope) and $b$ is the fixed cost (when $x = 0$), and $x$ is the quantity. Given $b=- 455$ (fixed cost is an expense, so it's negative in the profit function) and $x = 65$ at break - even.

Step2: Substitute values into profit formula

Substitute $P = 0$, $x = 65$ and $b=-455$ into $P(x)=mx + b$. We get $0=m\times65-455$.

Step3: Solve for $m$

Add 455 to both sides of the equation: $455 = 65m$. Then divide both sides by 65: $m=\frac{455}{65}=7$.

Answer:

$7$