Page 226 - How To Solve Word Problems In Calculus

original equation.

px + 6x + 7p = 5950

100p + 600 + 7p = 5950
107p = 5350

p = 50

Now we can solve for dp/dt:

dp dp
50(−2) + 100 + 6(−2) + 7 = 0
dt dt
dp
107 − 112 = 0
dt
dp 112
= ≈ 1.0467
dt 107

The price is increasing by approximately $1.05 per bushel per
day.

EXAMPLE 10
The demand x for milk (quarts), selling for p dollars per
quart at a supermarket is determined by the equation
px + 1200p − 6000 = 0. If the price is increasing at the rate
of 3 cents per week, at what rate is demand changing when
the price is $1.25 per quart?

Solution
Step 1
x = demand for milk (quarts)
p = price per quart (in dollars)

Step 2
dp dx
Given: = 0.03 Find: when p = 1.25
dt dt
Step 3
px + 1200p − 6000 = 0

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