'

Final

Exam Practice

Problems

Show all work in the

space below the

question.

Give

exact answers

unless

otherwise

indicated

1) Given

the following

supply and

demand equations:

S(p):80p

-80,

D(p)=

-100p

+

1000.

Find

the equilibrium price

and

quantity.

2) A machine

is

purchased

for

$20,000

and

depreciates

in value

$1,100

a

year.

If

V(t)

represents

the

value after t

years,

find:

a)

the equation

for

V(t),

b) the

value

after

5

years.

3) R(x)

:

300-100x-23x2

Represents

the revenue

for the

sale

of x

units

of a

grven

item

and

C(x):

(ll4)xa

-21x2 -133x+67

represents

the

total

cost

of

production

of

x units.

a) Find the profit,

P(x),

when x units

of that

itern

are sold

in

simplest

form.

b) Compute

P'(x),

C'(x) and

P"(x)

P'(x)

=

P"(x)

=

c'(x):

c)

Find

the

marginal

profit

atx:12

d)

Find

the

marginal

cost at

x:12

e)

Find the

sales level,

x, that

produces

the

maximum profit

and

justify

you

answer.

f) Find

the maximum

profit.

(nearest

dollar)