The total profit (in dollars) from the sale of x answering machines is P(x)=20x−0.6x2−260.

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

I assume the equation for the total profit is P(x) = - (0.6x)² + 20x - 260 as there was a formatting issue.

To find the exact profit from the sale of the 26th machine only, we subtract the total profit from the sale of the 25th machine from that of the 26th machine. This will give the exact profit of the 26th machine sale.

P(26) - P(25) = - (0.6*26)² + 20*(26) - 260 + (0.6*26)² - 20*(26) + 260 = $1.64

To find the marginal profit from the 26th machine sale, we first calculate the derivative of the function P(x).

P'(x) = -(0.6)²(2)x + 20 = 20 - 0.72x

P'(26) = 20 - 0.72*26 = $1.28

Thus, the exact profit of the 26th machine is $1.64 while the marginal profit is $1.28.