Page 223 - How To Solve Word Problems In Calculus

The actual cost of producing the 21st unit =
C(21) − C(20) = $207.10 − $200.00 = $7.10.
(b) Since x units will be sold when the price is p(x) dollars,

R(x) = xp(x)

= x(25 − 0.05x)
= 25x − 0.05x 2

R (x) = 25 − 0.1x

R (20) = $23.00

The actual revenue derived from the 21st unit =
R(21) − R(20) = $502.95 − $480.00 = $22.95.

Related Rates
As we saw in Chapter 3, the rate at which one quantity changes
is often related to the rate of change of other quantities. The
following steps outline the procedure for solving a related rates
business problem.

Step 1
Label all variables with an appropriate symbol. (In busi-
ness problems, diagrams are often inappropriate. However,
all variables should be clearly labeled for reference.)

Step 2
Determine which rates are given and which rate you
need to find. Write them down for future reference.

Step 3
Determine an equation (or several equations) relating
the variables defined in step 1.

Step 4
Differentiate the equation(s) in step 3 with respect to
time.

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