Page 220 - How To Solve Word Problems In Calculus

Solution
q

C (q) = 500 − 500e − 10
C (20) = 500 − 500e −2

= 500 − 67.67

= 432.33

His cost is increasing at the rate of $432.33 per unit.

Marginal Analysis in Economics
In economics, the marginal cost (MC) of producing an item is
the rate at which its cost changes with respect to the number of
items produced. Thus if C(x) is the cost of producing x items,
the marginal cost is C (x). Similarly, if R(x) and P(x) represent

the revenue and profit, respectively, in selling a quantity of x
units, then R (x) represents marginal revenue (MR) and P (x)

marginal profit (MP).
EXAMPLE 5
2
It costs 0.05x + 6x + 100 dollars to produce x pounds of
soap. Because of quantity discounts, each pound sells for
12 − 0.15x dollars. Compute the marginal cost, marginal
revenue, and marginal profit when x = 10.

Solution
2
C(x) = 0.05x + 6x + 100

MC(x) = C (x) = 0.1x + 6
MC(10) = $7.00
R(x) = (price per pound)(number of pounds sold)

= (12 − 0.15x)(x)

= 12x − 0.15x 2
MR(x) = R (x) = 12 − 0.3x

MR(10) = $9.00

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