The marginal profit for selling x souvenir hats is modeled by P'(x)=5-0.02x dollars. If fixed cost is 250 dollars, how do you find the number of hats you would like to sell to maximize profit? Then how do you find the profit for selling that many units? Would you take the antiderivative of the given function and plug in the found value to that?

Question

The marginal profit for selling x souvenir hats is modeled by P'(x)=5-0.02x dollars. If fixed cost is 250 dollars, how do you find the number of hats you would like to sell to maximize profit?  Then how do you find the profit for selling that many units?  Would you take the antiderivative of the given function and plug in the found value to that?

oobleck · Accepted Answer

p'(x) = 5 - 0.02x p(x) = 5x - 0.01x^2 - 250 max profit is where p'(x) = 0, or when x = 250 p(250) = 375