UNIVERSITY OF TECHNOLOGY, JAMAICA
SCHOOL OF MATHEMATICS & STATISTICS
MODULE: CALCULUS FOR SOCIAL SCIENCES (MAT1045)
WORKSHEET # 4
SEMESTERS 1&2 or Summer Session
Marginal Cost, Marginal Revenue and Marginal Profit
Question 1
If the total-cost function for a manufacturer is given by C (q)  8q 2  3q  2000
(a)
Find the marginal cost function
(b)
What is the marginal cost when q = 10?
(c)
Interpret your answer in (b).
Question 2
If the average-cost function for Pens R Us company is given by
c  4q  10 
7000
q
where q is the number of pens manufactured and c is expressed in dollars per pen.
(a)
Find the marginal-cost function.
(b)
Find the marginal cost when q =20 and interpret your result.
Question 3
Mullings & Williams Inc. manufactures widgets. The average cost function of this company is
given below:
250
c  0.001q 2  0.2q  20 
,
5  q  100
q
where q is the number of units of widgets, and c is expressed in dollars per unit.
(i)
(ii)
(iii)
Find the marginal cost function of the company.
What is the marginal cost when 50 widgets are produced?
Interpret your answer in (ii)
Question 4
If the demand equation for a monopolist’s product is p  300  0.4q
where p is the price per unit in dollars when q units are demanded.
Calculate the value of q for which revenue is a maximum.
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Question 5
Razor Sharp Ltd. is informed by a consultant that its annual profit is given by
   100, 000  5, 000q  0.25q 2 ,
where q is the number of disposable razor blades the company sells each year. Additionally, the
number of disposable razor blades the company can manufacture each year depends on the
number n of assembly – line workers it employs and is given by q  30n  0.01n2
d
Use the chain rule to find
.
dn
Question 6
A marketing research company estimates a demand for pens using the following model:
Q( p)  1500  5 p 2 ,
where p is the price in dollars.
(i) What price will give the maximum revenue?
(ii) Calculate the maximum revenue at this price.
Question 7
Given that the demand equation for “Ripped Jeans” is p  400  2q and the
cost function is C  4q  0.2q 2  400 , where q is the number of jeans sold,
and both p and C are expressed in dollars.
(i)
(ii)
(iii)
Calculate the number of jeans to be sold to obtain maximum profit.
Calculate the price at which this maximum profit occurs
Determine the maximum profit.
Question 8
Given that the demand function for a monopolist’s product is p  2q 2  10q  1000 and the
average-cost function is c  2q 2  36q  1600 
20
, where q is number of units, and both p and
q
c are expressed in dollars per unit.
(i)
(ii)
(iii)
Determine the level output at which profit is maximized.
Determine price at which maximum profit occurs.
Determine the maximum profit.
Revised March 2016 School of mathematics and Statistics
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