Project 16
MAC 2311
1. Suppose the daily supply
x
of a certain product in an open-air market is related to the unit
price
p
(in dollars) by the equation
100
p
2
+ 10
xp
=
x
2
+ 500
.
Calculate
dx
dp
implicitly. What rate of change does it represent?
Find all the points on the graph of the equation having
p
-coordinate
3
. Evaluate
dx
dp
at any
point that makes sense in the current context.
Now suppose the price of the product is rising by
50
cents per day when the price is $
3
.
Calculate the rate at which the daily supply is changing per day.
Suppose the daily demand for the product is given by the relationship
10
p
2
+ 3
x
2
= 1290
.
Calculate the rate at which the daily demand is changing at the instant described above.
What about the change in revenue?
2. Newton’s Law of Gravitation states that the force
F
exerted by a body of mass
m
on a body
of mass
M
has magnitude:
F
=
GMm
r
2
where
G
is the gravitational constant and
r
is the distance between the centers of the bodies.
Suppose a rocket is launched from earth so that when it is

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