Question

Let C ( q ) represent the cost and R ( q ) represent the revenue, in dollars, of producing q items. Suppose C ( 100 ) = 4000 and R ( 100 ) = 5500. If C ′ ( 100 ) = 20 and R ′ ( 100 ) = 24, approximately how much profit is earned by producing 101 items?

Answer 1

Answer:

$1,504

Step-by-step explanation:

The marginal profit for producing the 100th unit is given by:

$P' = R'(100) - C'(100)=24-20\\P'=\ 4$

Therefore, it is fair to assume that the 101st unit will produce an additional $4 profit.

The profit for producing the first 100 units is given by:

$P(100) = R(100)-C(100)\\P(100) = 5,500-4,000\\P(100) =\ 1,500$

Finally, the approximate profit for producing 101 items is:

$P(101) = P(100)+P'(100) = 1,500+4\\P(101) = \ 1,504$

Profit is approximately $1,504.