Calculus Business Application Worksheet
1.
A manufacturer makes fuel tanks for cars. The total weekly costs for the company to
produce x tanks is C  x   10000  90 x  .05x
a.
b.
c.
d.
e.
2
Find the marginal cost function.
Use the marginal cost function to estimate the cost of the 501st tank.
What is the cost to produce 400 tanks?
Find the average cost to produce 700 tanks.
Find the exact cost of the 501st tank.
2. A company comes up with the following formula to describe the demand
for a product at a particular price level. x  10000  1000 p , where x is the
number of units and p is the price per unit. The cost function for the
product is C  x   7000  2x .
a.
b.
c.
d.
e.
f.
g.
h.
Find the domain for the demand function.
Find the marginal cost function.
Find the revenue function.
Find the marginal revenue function.
Use the marginal revenue function at x=5000. What does it mean?
Find the profit function.
Maximize the profit function.
Find the average profit you make for producing 2000 units.
3.
The owner of a perfume company finds the demand function for a certain kind of perfume is
x
500
2
. She also has a cost function of C  x   .2 x  3x  200 .
p3
a.
b.
c.
d.
Find a function for the profit as a function of x bottles of skunk oil sold.
At what rate is the profit changing when you sell 12 bottles?
At what rate is the profit per bottle changing when you sell 12 bottles?
How many bottles should be sold to maximize profit?
4. A company plans to sell some new speakers. The demand function for them is
x  20000  25 p .
a. Find the revenue function.
b. Find the marginal revenue. What does R  30 mean?
c. How much revenue comes in when you sell 300 speakers?