Applied Mathematics for Business and Economics

Lecture Note Function

b. The revenue function is found by multiplying the price for one item by the

number of items sold.

Rx P x()=×= − = −( 200 xx) 200 x x^2

c. Profit is the difference between revenue and cost

() () ()

()()

2

2

200 500 140

60 500

Px Rx Cx

xx x

xx

=−

=−−+

=− + −

d. To find the break- event, set the revenue equal to the cost and solve for x

() ()

()()

2

2

200 500 140

60 500 0

10 50 0

10 or 50

Rx Cx

xx x

xx

xx

xx

=

−= +

−+=

−−=

==

This model shows that a profit occurs if the company produces between 10 and 50
items. We will discuss calculus techniques for maximizing profit later.

4.4 Market Equilibrium .................................................................................

An important economic application involving intersections of graphs arises in
connection with the law of supply and demand. In this context, we think of the
market price p of a commodity as determining the number of units of the commodity
that manufacturers are willing to supply as well as the number of units that consumers
are willing to buy. In most cases, manufacturers’s supply increases and

consumers’demand decreases as the market price p increases. See the figure.

Sp()

Dp()

q

Supply: qSp= ( )

Equilibrium

point

The point of intersection of the supply and demand curves is called the point of
market equilibrium. The p coordinate of this point (the equilibrium price) is the

•

Shortage Surplus

Demand: qDp= ( )

p p

Equilibrium

price