TUTORIAL 8
1.) Find the coordinates of all turning
points and determine the nature of the turning
points
a.) y = 0.5 x 2 - 8x + 60
b.) y = 4x + 64/x
2.) A firm has determined that total
revenue is a function of the price charged for its
product. Specifically, the total revenue function is:
R
= - 20 p 2 + 1,960p
where p equals the price in dollars
a.)
Determine the price p which results in total maximum revenue
b.)
What is the total maximum revenue?
3.) The demand function for a particular
output is given by p = 1800 - 100q where p
is the price per unit and q is the quantity demanded
a.)
Find the total revenue function
b.)
Calculate the maximum revenue
4.) If fixed costs are 4, variable costs
per unit are 1 and demand function is
p
= 10 - 2q,
a.)
Obtain an expression for the total profit, p, in terms of q
b.)
For what values of q does the firm breakeven?
c.)
What is the maximum profit?
5.) At a selling price of $3.80 per unit,
the expected sales of a particular product
would be 10,200 units. It would have fallen to 8,400 if the
selling price was
$4.70. The total cost
function for the product is given by C = 15000 + 1.8q,
where q is the units of output produced.
a.)
Derive the demand function, assuming it is linear
b.)
Derive the total revenue function
c.)
Derive the total profit function
d.)
Calculate the price per item at a demand level of 9500
e.)
What is the maximum profit and the corresponding level
of output?
f.)
What price per unit should the firm charge at the maximum profit point?
6.) Suppose the cost equation for
manufacturing a calculator is C = 100,000 + 20q
and the demand equation is q = 48,000 –
400p, where q is the number of units sold per month at a price of RM p per
unit.
a.)
Derive
the revenue function
b.)
Find
the profit function
c.)
Calculate
the breakeven points
d.)
What
is the monthly profit or loss for a production level of:
i.
10,000
units?
ii.
20,000
units
iii.
40,000
units
e.)How many units should be sold in order to obtain the
maximum profit?
f.)
What is the amount of maximum profit obtained?
7.) The total cost of producing q units
of a certain product is described by the
function C = 4,000 + 300q + 0.01q2
where C is the total cost stated in dollars
a.)
How many
units of q should be produced in order to minimize the average cost per unit?
b.)
What
is the minimum average cost per unit?
c.)
What
is the total cost of production at this level of output?
8.) The total cost ( C
) and total revenue ( R ) functions for a product are:
C
= 50,000 + 20q + 0.0001q2
R
= 60q – 0.004q2
a.)
Find
the marginal cost and marginal revenue function
b.)
Using
the marginal approach, determine the profit maximizing level of output.
9.) The annual profit for a firm depends
upon the number of units produced.
Specifically,
the function which describes the relationship between the profit p
and the number of units produced, q, is:
p = -0.12q2 + 6000q –
25,000,000
a.)
How
many units should be produced to maximize profit?
b.)
What
is the expected maximum profit?
10.) The cost of building an office
block, x floors high, is made up of three
components:
1.
$10
million for the land
2.
$1/4
million per floor
3.
specialized
costs of $10,000x per floor
How many floors should
the block contain if the average cost per floor is to be minimized?
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