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**

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