Math 1313
Section 1.5
1
Section 1.5: Linear Models
An
asset
is an item owned that has value.
Linear Depreciation
refers to the amount of decrease in the book value of an asset.
The
purchase price
, also known as
original cost
, of an asset is the price paid for the asset when
purchased.
The
scrap value
of an asset is the remaining value after it is no longer seen as useable.
Example 1:
In 2010, the B&C Company installed a new machine in one of its factories at a cost of
$150,000. The machine is depreciated linearly over 15 years with no scrap value.
a. Find the rate of depreciation for this machine.
b. Find an expression for the machine’s book value in the t-th year of use (0 < t < 15).
Example 2:
A company’s car has an original value of $85, 000 and will be depreciated linearly over 6
years with scrap value of $10,000.
a. Find the expression giving the book value of the car at the end of year t (0 < t < 6).
b. Find the car’s book value in at the end of the third year.

Math 1313
Section 1.5
2
Linear Cost, Revenue and Profit Functions:
If
x
is the number of units of a product manufactured or sold at a firm then,
The
cost function
, C(x), is the total cost of manufacturing x units of the product.
Fixed costs
are the costs that remain regardless of the company’s activity.
Examples: building fees (rent or mortgage), executive salaries
Variable costs
are costs that vary with the production or sales.
Examples; wages of production staff, raw materials
The
revenue function
, R(x), is the total revenue realized from the sale of x units of the product.
The
profit function
, P(x), is the total profit realized from the manufacturing and sale of the x units of
product.