How to find profit function??

Question

Let C(x) = 3x + 350 and R(x) = 24x.

(a) Write the profit function P(x).

P(x) = 

 

(b) What is the slope m of the profit function?

m = 

(c) What is the marginal profit MP ?

MP = 

(d) Interpret the marginal profit.

Each additional unit sold decreases the profit by this much.Each additional unit sold increases the profit by this much.    This is the smallest number of units that can be sold in order to make a profit.The profit is maximized when this many units are sold.

Answer 1

Profit= R-C = 24x-(3x+350) = 24-3x-350

P(x)= 21x - 350

slope is the coefficient of the x term = 21

marginal profit is the same as the slope= 21

it's how much profit increases as x increases. It's the derivative of the profit function = dP/dx=P'(x)=21