Page 227 - How To Solve Word Problems In Calculus

Step 4
dx dp dp
p + x + 1200 = 0
dt dt dt

Step 5
When p = 1.25, we get, from step 3,

1.25x + 1200(1.25) − 6000 = 0
1.25x + 1500 − 6000 = 0

1.25x = 4500

x = 3600

From step 4,

dx
1.25 + 3600(0.03) + 1200(0.03) = 0
dt

dx
1.25 + 108 + 36 = 0
dt
dx
1.25 =−144
dt

dx
=−115.2
dt

The demand for milk decreases at the rate of 115.2 quarts
per week.

Optimization
Optimization problems are very important in business.
Whether we are trying to maximize our profit or minimize our
cost, knowing how to determine optimal values is extremely
useful.
The procedures illustrated in Chapter 4 for finding the
maximum or minimum value of a function extend in a very
natural way to business problems. We list the main steps for
review.

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