The total profit from the sale of x answering machines is P(x)=20x−0.2x2−260

Question

A) Find the exact profit from the sale of the 26th machine.

B) Use the marginal profit to approximate the profit from the sale of the 26th machine

Answer 1

A) to find the exact profit from the total profit function we need to find the total profit after selling 26 machines and subtract the total profit from selling 25 machines:

P(26)-P(25)=20*26-.2(26²)-260-(20*25-.2(25²)-260) = 520-135.2-260-500+125+260 = 20-10.2 = $9.80

B) to find the marginal profit we need to take the derivative and then plug in 25 (why 25? because we want find the slope i.e. the rate of change by selling one additional machine):

P'(x)=20-.4x; P'(25)=20-.4*25=$10