Page 31 - How To Solve Word Problems In Calculus

C(t) = 750 + 30t

P = 8x − 6t − 750

= 8(12t) − 6t − 750
= 96t − 6t − 750

P(t) = 90t − 750

EXAMPLE 12
A tour bus has 80 seats. Experience shows that when a tour
costs $300, all seats on the bus will be sold. For each addi-
tional $10 charged, however, 2 fewer seats will be sold. Find
a function that represents the revenue derived from a single
bus tour.

Solution
Step1
In this type of problem it is convenient to let x represent
the number of $10 increments above the base price of $300.
Thus, for example, if x = 2 the price is $320. We let n represent
the number of seats sold and p the price per seat.
Step2
The revenue R is the product of the number of seats sold
and the price per seat.

R = np

Step3
For each unit increment in x, n decreases by 2 and p in-
creases by 10.

n = 80 − 2x
p = 300 + 10x

Substituting into step 2,
R = np = (80 − 2x)(300 + 10x)

R(x) = 24,000 + 200x − 20x 2

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