Applications of Linear Equations

1
Applications of Linear Equations
Chapter 5
2
After completing this chapter, you will be able
to

• Solve two linear equations in two variables
• Solve problems that require setting up two
  linear equations in two variables
• Graph a linear equation in two variables
• Perform linear cost-volume-profit and
  break- even analysis employing
• The contribution margin approach
• The algebraic approach of solving the cost
  and revenue functions
• A break-even chart

3
Solving Two Equations in Two Unknowns
2x 3y 6 (1) x y 2 (2)
(1) 2x 3y 6 (2) ? 2 2x
2y 4 Subtract (1) (2) -5y
10 y 2
2x 3(2) 6 2x 6 6 x 0
Substitute y2 into equation (1)
You should always check your answer by
substituting the values into each of the
equations.
4
COST-VOLUME-PROFIT AND BREAK-EVEN ANALYSIS

• Fixed costs do not change if sales increase or
  decrease.
• rent
• management salaries
• some forms of depreciation expense
• property taxes

• Variable costs grow in direct proportion to the
  volume of sales. If unit sales increase by 10,
  total variable costs will increase by 10.
• materials costs
• direct labour costs in manufacturing
• wholesale cost of goods in retailing

5
Market research for a new product indicates that
the product can be sold at 50 per unit. Cost
analysis provides the following information
Fixed costs per period 8640 FC Variable
costs per unit 30 VC Production capacity per
period 900 units

• Calculate the breakeven point
• in units
• as a percent of capacity
• in

6
Contribution Margin Approach
How much does the sale of an additional unit of a
firms product contribute towards increasing its
net income?
CM SP - VC
CM contribution margin SP unit price NI net
income CR contribution rate X number of units
sold
NI SPX (FC VCX) At Breakeven, NI 0
CR CM/SP 100
At Breakeven, X FC / CM
7
So, in this example, SP 50 FC 8640 VC
30 Capacity 900
CM SP - VC
At Breakeven, X FC / CM
50 - 30 20
8640 / 20 432 units
B/E in units to B/E unit price
432 50 21 600
As a of capacity, B/E units to B/E /
units at capacity
432 / 900 100 48 of capacity
8
The lighting division of Seneca Electric Co.
plans to introduce a new street light based on
the following accounting information
FC 3136 VC 157. SP 185 Capacity 320
units

• Calculate the breakeven point
• in units
• as a percent of capacity
• in

9
B/E
X FC / CM
3136 / 28 112 units
B/E units to B/E unit price
112 185 20 720
B/E units to B/E / units at capacity
112 / 320 100 35 of capacity
10
Find the net income if the lighting division
sells 134 street lights.
FC 3136 VC 157. SP 185 Capacity 320
units
11
What unit sales will generate a net income of
2000?
FC 3136 VC 157. SP 185 Capacity 320
units
12
If the company experiences a loss of 336, find
the unit sales.
FC 3136 VC 157. SP 185 Capacity 320
units
13
Determine the profit or loss when the company
operates at 85 of capacity.
FC 3136 VC 157. SP 185 Capacity 320
units
14
Last year Marconi Printing had total sales of
375 000 while operating of 75 of capacity. The
total of its variable costs was 150 000. Fixed
costs were 180 000. What is Marchonis
breakeven point expressed in dollars of sales?
Let SP 1 and X represent the number of 1
units sold.
VC Total VC Total unit sales
150 000 375 000
TC FC VC
180 000 0.40X
0.40
NI CMX - FC 0.60X - 180 000
1.0
.40
At B/E, NI 0 0 0.60X - 180 000 B/E X
180 000 / 0.60 300 000 units
.60