Cost Functions
A cost function for a company for a certain commodity is given by the equation below. Find the total cost of producing 300 units.
C(x)=8000+200x-0.2x^2
$50,000
The relationship between the unit price, p, and the quantity demanded, x, of a couch is represented by the equation below. Determine the revenue made when 200 couches are sold.
p=-0.02x+400
$79,200
Match each of the following if the elasticity of demand is the number given.
1. E(p)=0.3 A. Unitary
2. E(p)=1 B. Elastic
3. E(p)=3 C. Inelastic
C, A, B
Find the relative rate of change of the function below at x=4
f(x)=x^2-5x+12
37.5%
Katie deposits $1200 in the bank. With an interest rate of 3% compounded quarterly, how much money will she have after 5 years?
$1,393.42
A cost function for a company for a certain commodity is given by the equation below. Find the actual cost of producing the 285th unit.
C(x)=8000+200x-0.2x^2
$86.20
The relationship between the unit price, p, and the quantity demanded, x, of a couch is represented by the equation below. Find the marginal revenue when 55 couches are sold.
p=-0.02x+400
$397.80 per couch
When the price of a commodity is raised, the percent change of demand changes by a smaller amount. Does this represent an elastic, inelastic, or unitary relationship?
Inelastic
Find the relative rate of change of the function below at x=12.
f(x)=sqrt(3x-20)
9.4%
An initial investment of $2500 at 5% interest is compounded monthly. How much interest will be earned if the money is left for 2 years?
$262.35
A cost function for a company for a certain commodity is given by the equation below. Find the average cost when 333 units are produced.
C(x)=8000+200x-0.2x^2
$157.42
The relationship between the unit price, p, and the quantity demanded, x, of a couch is represented by the equation below. The cost function is also shown below. Find the profit earned when 3005 couches are sold.
p=-0.02x+400
C(x)=100x+200,000
$520,899.50
The relationship between the unit price, p, in dollars and the quantity demanded, x, of a commodity is given below. Determine if the relationship is elastic, inelastic, or unitary for E(350).
x=20,000-50p
Elastic
How much money should be deposited in a bank paying interest at a rate of 6% per year compounded monthly so that at the end of 3 years, the accumulated amount will be $20,000?
$16,712.90
Find the interest rate needed for an investment of $5000 to grow to an amount of $6000 in 3 years if interest is compounded daily. Round to one decimal place for your percentage.
6.1%
A cost function for a company for a certain commodity is given by the equation below. Find the marginal cost when 300 units are produced.
C(x)=8000+200x-0.2x^2
$80 per unit
The relationship between the unit price, p, and the quantity demanded, x, of a couch is represented by the equation below. The cost function is also shown below. Find the marginal profit when 3880 couches are sold.
p=-0.02x+400
C(x)=100x+200,000
$144.80 per couch
The relationship between the unit price, p, in dollars and the quantity demanded, x, of a commodity is given below. Find E(375)
x=20,000-50p
15
How much money should be deposited in a bank paying interest at a rate of 2.5% per year compounded daily so that at the end of 4 years, the accumulated amount will be $1,000?
$904.84
Find the accumulated amount after 3 years if $1000 is invested at 8% per year compounded continuously.
$1271.25
A cost function for a company for a certain commodity is given by the equation below. Graph the cost function and determine the number of units to reach the maximum cost, and what the maximum cost is.
C(x)=8000+200x-0.2x^2
500 units at $58,000
The relationship between the unit price, p, and the quantity demanded, x, of a couch is represented by the equation below. The cost function is also shown below. Graph the profit function and find the number of units required to reach maximum profit, and what the maximum profit is. (Use window from 0 to 200,000)
p=-0.02x+400
C(x)=100x+200,000
Maximum at 7500 units of $925,000
The relationship between the unit price, p, in dollars and the quantity demanded, x, of a commodity is given below. Find E(80).
p=125-x^2
8/9
How much money should be deposited in a bank paying interest at a rate of 3.852% per year compounded semiannually so that at the end of 6 months, the accumulated amount will be $50,500?
$49,545.75
Option A: rate of 4% compounded weekly.
Option B: rate of 3.8% compounded continuously.
What is the difference between these two options and which option should he choose?
Difference of $14.66, he should choose option A.