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16 CHAPTER 1 INTRODUCTION

on and varies with the production volume. To illustrate how cost and volume models
can be developed, we will consider a manufacturing problem faced by Nowlin Plastics
in Shanghai. Nowlin Plastics produces a variety of compact disc (CD) storage cases.
Nowlin’s bestselling product is the CD-50, a slim, plastic CD/DVD holder with a
specially designed lining that protects the optical surface of the disc. The holders are
sold in units of 50 cases. Several products are produced on the same manufacturing
line, and a setup cost is incurred each time a changeover is made for a new product.
Suppose that the setup cost for the CD-50 is E3000. This setup cost is a fixed cost
that is incurred regardless of the number of units eventually produced. In addition,
suppose that labour and material costs are E2 for each unit produced. The cost-volume
model for producing x units of the CD-50 can be written as:

CðxÞ¼ 3000 þ 2x (1:2)

where
x = production volume in units
C(x) = total cost of producing x units
Once a production volume is determined, the model in Equation (1.2) can be
used to calculate the total production cost. For example, management have an order
for 1200 units (x ¼ 1200) and using equation (1.2) we can see that this would result
in a total cost of C(1200) ¼ 3000 + 2(1200) ¼ E5400.
Marginal cost is defined as the rate of change of the total cost with respect to
production volume. That is, it is the cost increase associated with a one-unit increase
in the production volume. In the cost model of Equation (1.3), we see that the total
cost C(x) will increase by E2 for each unit increase in the production volume. Thus,
the marginal cost is E2. With more complex total cost models, marginal cost may
depend on the production volume. In such cases, we could have marginal cost
increasing or decreasing with the production volume x.
Revenue and Volume Models

Management of Nowlin Plastics will also want information on the projected revenue
associated with selling a specified number of units – a model of the relationship
between revenue and volume is also needed. Each case of CD-50 units sells for E5.
The model for total revenue can now be written as:

RðxÞ¼ 5x (1:3)

where
x = sales volume in units
R(x) = total revenue from selling x units

Marginal revenue is defined as the rate of change of total revenue with respect to
sales volume. That is, it is the increase in total revenue resulting from a one-unit
increase in sales volume. In the model of Equation (1.3), we see that the marginal
revenue is E5. In this case, marginal revenue is constant and does not vary with the
sales volume. With more complex models, we may find that marginal revenue
increases or decreases as the sales volume x increases.

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