Page 225 - How To Solve Word Problems In Calculus

Step 5
dC 250 750
When x = 50, = √ · 3 = = 18.75.
dt 2500 − 900 40
The cost of advertising is increasing at the rate of $18,750 per
month.

EXAMPLE 9

The wholesale price p of string beans, in dollars per bushel,
and the daily supply x, in thousands of bushels, are related by
the equation

px + 6x + 7p = 5950

If the supply is decreasing at the rate of 2000 bushels per day,
at what rate is the daily bushel price changing when 100,000
bushels are available? Is the price increasing or decreasing?

Solution
Step 1
x = supply of string beans (thousands of bushels)
p = price per bushel (dollars)

Step 2
dx
Given: =−2
dt dx/dt is negative, since
supply is decreasing.
dp
Find: when x = 100
dt
Step 3
px + 6x + 7p = 5950

Step 4
dx dp dx dp
p + x + 6 + 7 = 0 ← We use the product rule to
dt dt dt dt find the derivative of px.
Step 5
We know the values of x and dx/dt and we are look-
ing for dp/dt. To find p when x = 100 we go back to the

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