Question

Link has a business selling swords he has collected on his various journeys. He determines his marginal revenue to be ?′(?) where ? is the number of swords he sells, while ?′(?) is his marginal cost.

Write a sentence that indicates the meaning of the expression ∫ (? ′ (?) − ? ′ (?)) 15 10 ??. Be as specific as possible.

Is it possible for ∫ (? ′ (?) − ? ′ (?))?? 15 10 to be negative? Write a sentence to explain what it would mean if this integral were negative.

Answer 1

Solution :- Given marginal revenue = ?′(?) and  marginal cost = ?′(?)

We know that Profit P(x) = R(x) - C(x) and

Marginal profit  P'(x) = R'(x) - C'(x)

the expression ∫ (? ′ (?) − ? ′ (?)) from 10 to 15 represents the total profit obtained by selling the swords from 10 to 15 .

b) Is it possible for ∫ (? ′ (?) − ? ′ (?))?? 15 10 to be negative ? yes it may be but often it is not possible because every firm wants to earn profit .

∫ (? ′ (?) − ? ′ (?))?? 15 10 to be negative . it means the cost of producing from 10 to 15 swords is greater then the Revenue earned from selling 10 to 15 swords .

Note that in general it is not possible