what is the profit and marginal cost?

Question

Your monthly profit (in dollars) from selling magazines is given by

P = 8x +x

where x is the number of magazines you sell in a month. If you are currently selling x = 50 magazines per month, find your profit and your marginal profit. (Round your answers to two decimal places.)

profit=___

marginal profit=___ per additional magazine

Answer 1

Hi Alice S.

So you need to just substitute in your sales into the given P equation and calculate your profit (that's your total profit, if you want profit per magazine divide by 50).

Marginal profit = the first derivative of the profit, evaluated at x=50.

Are you new to calculus? If so, you need to know how to take the derivative of am algebraic exrpression. For each term in the expression of form ax^n, the first derivative is anx^(n-1). So for your P equation, P ' (x) = 8*1*x^0 +(1/2)x^(-1/2) . That evaluates to 8 + (1/2)/(50)^(1/2) , or about 8.07071067812 , rounds to $8.07 . If you think about the meaning of a derivative (or, graphically, a slope of a function) you will see that that figure is inherently "per magazine".

If that sounds like a lot of money, consider that in times of economic hardship, subscribers tend to cancel, which is exactly when you might be needing to maximize your own profits ....

-- Cheers, -- Mr. d.