Transcript 1.5 Calculus Section 1.5x

Economic Definitions
Profit = Revenue – Cost
P(x) = R(x) – C(x)
•
•
•
•
Assume the cost of producing x radios is C(x) = .4x2 +7x + 95 dollars.
A. Find the cost of producing 20 radios.
B. Determine the cost of producing the 20th radio.
C. Determine the cost of producing 0 radios.
It costs a manufacturer C(x) = .4x2 +7x + 95 dollars to produce x radios. Each radio can be
sold for $40.
a. Determine the profit function.
b. What is the profit on the manufacture and sale of 25 radios?
c. What is the profit on the 25th radio?
Break Even Point occurs when the profit is zero or when
revenue equals costs.
Break even: P(x) = 0 or R(x) = C(x)
A manufacturer of plastic
containers for compact
disks has a profit function
P(x) = .3x – 150, where x is
the number of CD
containers produced and
sold. How many containers
must be made and sold to
break even.
The cost and revenue function for a business are given by
C(x)=20x + 1250 and R(x)=50x -.1x2. For what value of x will the
business break even?
The relationship between price and consumer demand is given
by a demand equation. This equation is usually some type of
inverse variation. As the price increases, the demand decreases.
The relationship between the
price per unit to a supplier and
the number of items supplied
is given by a supply function.
This equation is usually some
type of direct variation. As
price increases, supply
increases.
Revenue is the money that is earned by selling x items
of a product.
Revenue is the product of the number of items sold and the
price of each item.
R(x) = x ∙ p
x = number of items sold
p = price per item
Use the demand function p=80-.2x to construct the revenue
function and then find the total revenue from the sale of 90
units.
The total cost function is the product of the number of
items produced and the cost per item plus the fixed costs.
C(x) = x∙ p + (fixed costs)
x=number of items
p=cost per item
Use the supply function p=.02x+3 to construct the
cost function, then find the total cost of supplying 85
units. Assume there are no fixed costs.
Equilibrium Point occurs when the supply of a product
equals the demand of the product. (Supply is the
amount that producers are willing to produce and sell.
Demand is the amount that consumers are willing to
buy.)
Suppose the demand function for a product is p=17-.2x and the
supply equation is p=.4x+8.
a. Find the equilibrium quantity.
b. Find the equilibrium price.
c. Find the equilibrium point.
assignment
•
•
•
•
Page 50
Problems 2-14 even, 18,20,24,28,30,32
Page 52
Problems 2,4