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CHAPTER 3
Analysis of Cost, Volume, and
Pricing to Increase
Profitability
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Learning Objective
LO1LO1
To use the contribution margin per unit
approach to calculate the sales volume
required to break even or earn a target profit
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Determining the Contribution Margin per Unit
Bright Day produces one product called Delatine. Delatine is a nonprescription herb mixture. The
contribution margin per bottle of Delatine is:
Sales revenue per bottle 36$ Variable cost per bottle 24 Contribution margin per bottle 12$
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Determining the Break-even Point
Bright Day uses a cost-plus-pricing strategy; it sets prices at cost plus a markup of 50% of cost. Delatine costs $24 per bottle to manufacture, so
a bottle sells for $36 ($24 + [50% × $24]).
Sales revenue per bottle 36$ Variable cost per bottle 24 Contribution margin per bottle 12$
The company’s first concern is if it can sell The company’s first concern is if it can sell enough bottles of Delatine to cover its fixed costs enough bottles of Delatine to cover its fixed costs
and make a profit!and make a profit!
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Determining the Break-even Point
The break-even point is the point where total total revenue equals total costsrevenue equals total costs (both variable and
fixed). For Bright Day, the cost of advertising is estimated to be $60,000. Advertising costs are
the fixed costs of the company. We use the following formula to determine the break-even
point in units.
The break-even point is the point where total total revenue equals total costsrevenue equals total costs (both variable and
fixed). For Bright Day, the cost of advertising is estimated to be $60,000. Advertising costs are
the fixed costs of the company. We use the following formula to determine the break-even
point in units.
Break-evenBreak-evenvolume in unitsvolume in units==
Fixed costsFixed costsContribution margin per Contribution margin per
unitunit
= $60,000$12
= 5,000 units5,000 units
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Determining the Break-even Point
For Delatine, the break-even point in sales dollars is $180,000 (5,000 bottles × $36 selling price).
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Determining the Break-even Point
Once all fixed costs have been covered (5,000 bottles sold), net income will increase by $12 per $12 per
unit contribution margin.unit contribution margin.
What will be the increase in net income if units sold What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?increase from 5,000 units to 5,600 units?
What will be the increase in net income if units sold What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?increase from 5,000 units to 5,600 units?
$12$12
4,998 4,999 5,000 5,001 5,002 Revenue @ $36 179,928$ 179,964$ 180,000$ 180,036$ 180,072$ Variable Expenses @ $24 (119,952) (119,976) (120,000) (120,024) (120,048) Contribution Margin @$12 59,976 59,988 60,000 60,012 60,024 Fixed Expenses (60,000) (60,000) (60,000) (60,000) (60,000) Net Income (24)$ (12)$ -$ 12$ 24$
Number of Units Sold
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Determining the Break-even Point
What will be the increase in net income if units What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?sold increase from 5,000 units to 5,600 units?
What will be the increase in net income if units What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?sold increase from 5,000 units to 5,600 units?
New Units Sold 5,600 Previous Units Sold 5,000 Increase in Units Sold 600 Contribution Margin Per Unit 12$ Increase in Income 7,200$
Number of Units Sold5,000 5,600
Revenue @ $36 180,000$ 201,600$ Variable Expenses @ $24 (120,000) (134,400) Contribution Margin @$12 60,000 67,200 Fixed Expenses (60,000) (60,000) Net Income -$ 7,200$
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Reaching a Target Profit
Bright Day’s president wants the advertising campaign to produce profits of $40,000 to the
company.Break-evenBreak-even
volume in unitsvolume in units== Fixed costs + Fixed costs + Desired Desired
profitprofit Contribution margin Contribution margin per unitper unit
=$60,000 + $40,000
$12
= 8,333.33 units8,333.33 unitswhich rounds towhich rounds to
8,334 whole units8,334 whole units
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Reaching a Target Profit Level
At $36 per unit selling price, the sales dollars are equal to $300,000, as shown below:
IncomeUnits sold 8,334 Revenue @ $36 300,024$ Variable Expenses @ $24 (200,016) Contribution Margin @$12 100,008 Fixed Expenses (60,000) Net Income 40,008$
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Check Yourself Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of
lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Matrix profit in the coming month of $37,500. Matrix must sell the following number of must sell the following number of lawnmowers:lawnmowers:
1.1. 3,000.3,000.
2.2. 3,500.3,500.
3.3. 4,000.4,000.
4.4. 4,500.4,500.
Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Matrix profit in the coming month of $37,500. Matrix must sell the following number of must sell the following number of lawnmowers:lawnmowers:
1.1. 3,000.3,000.
2.2. 3,500.3,500.
3.3. 4,000.4,000.
4.4. 4,500.4,500.
$225,000 + $225,000 + $37,500$37,500
$75$75
= 3,500= 3,500
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Learning Objective
LO2LO2
To set selling prices by using
cost-plus, prestige, and target profit
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Assessing the Pricing Strategy
Cost-Plus Pricing
Prestige Pricing
Target Pricing
Price products at variable cost plus some percentage of the
variable, normally 50%.
Price products with a premium because the product is new or has a prestigious name brand.
Price products at the market price and then control costs to
be profitable at the market price.
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Assessing the Pricing Strategy
The Marketing Department at Bright Day The Marketing Department at Bright Day suggests that a price drop from $36 per bottle suggests that a price drop from $36 per bottle
to $28 per bottle will make Delatine a more to $28 per bottle will make Delatine a more attractive product to sell. The president wants attractive product to sell. The president wants to know what effect such a price drop would to know what effect such a price drop would
have on the company’s stated goal of have on the company’s stated goal of producing a $40,000 profit.producing a $40,000 profit.
You have been asked to determine the You have been asked to determine the number of bottles that must be sold to earn number of bottles that must be sold to earn
the $40,000 profit at the new $28 selling price the $40,000 profit at the new $28 selling price per bottle. See if you can provide an answer per bottle. See if you can provide an answer
to the president before going to the next to the president before going to the next screen!screen!
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Effects of Changes in Sales Price
New Selling Price Per Bottle 28$ Variable Expenses Per Bottle 24 New Contribution Margin 4$
Step 1
Break-evenBreak-evenvolume in unitsvolume in units=
= Fixed costs + Fixed costs + Desired Desired profitprofit Contribution margin Contribution margin
per unitper unit
Step 2
=$60,000 + $40,000
$4
= 25,000 units25,000 units
Step3
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Effects of Changes in Sales Price
The required sales volume in dollars is $700,000 (25,000 units × $28 per bottle) as shown below:
IncomeUnits sold 25,000 Revenue @ $28 700,000$ Variable Expenses @ $24 (600,000) Contribution Margin @$4 100,000 Fixed Expenses (60,000) Net Income 40,000$
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Learning Objective
LO3LO3
To use the contribution margin per unit to conduct cost-volume-profit
analysis
The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin
3-18Assessing the Effects of Changes in Variable Costs
Bright Day is considering an alternative mixture for Delatine along with new
packaging. This new product would sell for $28 per bottle and have a variable cost per
bottle of $12. The president is not in favor of the new product but wants to know how many units must be sold to produce the
desired profit of $40,000.
You have been asked to determine the units that must be sold and the total sales revenue
that will be produced!
The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin
3-19Assessing the Effects of Changes in Variable Costs
New Selling Price Per Bottle 28$ Variable Expenses Per Bottle 12 New Contribution Margin 16$
Step 1
Break-evenBreak-evenvolume in unitsvolume in units=
= Fixed costs + Fixed costs + Desired Desired profitprofit Contribution margin Contribution margin
per unitper unit
Step 2
=$60,000 + $40,000
$16
= 6,250 units6,250 units
Step3
The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin
3-20Assessing the Effects of Changes in Variable Costs
At $28 per unit selling price, the sales dollars are equal to $175,000 as shown below:
IncomeUnits sold 6,250 Revenue @ $28 175,000$ Variable Expenses @ $12 (75,000) Contribution Margin @$16 100,000 Fixed Expenses (60,000) Net Income 40,000$
The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin
3-21Assessing the Effects of Changes in Fixed CostsBright Day’s president has asked you to determine the required sales volume if
advertising costs were reduced to $30,000, from the planned level of $60,000.
= $30,000$30,000 + $40,000
$16
= 4,375 units4,375 unitsBreak-even
volume (units)
IncomeUnits sold 4,375 Revenue @ $28 122,500$ Variable Expenses @ $12 (52,500) Contribution Margin @$16 70,000 Fixed Expenses (30,000) Net Income 40,000$
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Learning Objective
LO4LO4
To draw and interpret a cost-
volume-profit graph
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Cost-Volume-Profit Graph
Units sold - 5,000 10,000 Revenue @ $36 -$ 180,000$ 360,000$ Variable Expenses @ $24 - (120,000) (240,000) Contribution Margin @$12 - 60,000 120,000 Fixed Expenses (60,000) (60,000) (60,000) Net Income (60,000)$ -$ 60,000$
Income at Various Levels
Information to prepare a break-even Excel graph.Units sold - 5,000 10,000
Revenue - 180,000 360,000 Total Cost 60,000 180,000 300,000 Fixed Cost 60,000 60,000 60,000
We have developed income statements for zero sales, break-even sales, and ten thousand units.
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Cost-Volume-Profit Graph
Break-even Graph
-
100,000
200,000
300,000
400,000
- 5,000 10,000
Units Sold
Do
llars
Revenue
Total Cost
Fixed Cost$180,000$180,000
5,000 units5,000 units
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Cost-Volume-Profit Graph
Break-even Graph
-
100,000
200,000
300,000
400,000
- 5,000 10,000
Units Sold
Do
llars
Revenue
Total Cost
Fixed Cost
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Learning Objective
LO5LO5
To calculate margin of safety
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Calculating the Margin of Safety
The margin of safety measures the cushion between budgeted sales and the break-even point. It quantifies the amount by which actual sales can fall short of expectations before the company will
begin to incur losses. With a selling price of $28 per unit and variable costs of $12 per unit, and a
desired profit of $40,000, budgeted sales were:= $30,000$30,000 +
$40,000$16
= 4,375 units4,375 unitsBreak-even
volume (units)
Break-even unit sales assuming no profit would be:
= = 1,875 units1,875 units$30,000$30,000 $16
Break-evenvolume (units)
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Calculating the Margin of Safety
In Units In DollarsBudgeted sales 4,375 122,500$ Break-even sales (1,875) (52,500) Margin of safety 2,500 70,000$
Margin ofsafety
=Budgeted sales – Break-even
salesBudgeted sales
Margin ofsafety
=$122,500 –
$52,500$122,500
= 57.14%57.14%
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Management considers a new product, Delatinethat has a sales price of $36 and variable costs
of $24 per bottle. Fixed costs are $60,000. Break-even is 5,000 units.
Management wants to earn a $40,000 profit onDelatine. The sales volume to achieve this
profit level is 8,334 bottles sold.
Marketing advocates a target price of $28 perbottle. The sales volume required to earn a$40,000 profit increases to 25,000 bottles.
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Target costing is employed to reengineer theproduct and reduces variable cost per unit to
$12. To earn the desired profit of $40,000, salesvolume decreases to 6,250 units.
Target costing is applied and fixed costs arereduced to $30,000. The sales volume to earn
the desired $40,000 profit is 4,375 units.
In view of the 57.14% margin of safety,management decides to add Delatine to its
product line.
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Learning Objective
LO6LO6
To conduct sensitivity analysis for cost-volume-
profit relationships
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Performing Sensitivity Analysis Using Spreadsheet Software
After reviewing the spreadsheet analysis, Bright Day’s management team is convinced it should undertake radio
advertising for Delatine.
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Learning Objective
LO3LO3
To use the contribution margin per unit to conduct cost-volume-profit
analysis
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3-34
Decrease in Sales Price with an Increase in Sales Volume
The marketing manager believes reducing the sales price per bottle to $25 will increase sales volume by 625 units. Previous sales volume was:
= $30,000$30,000 + $40,000
$16
= 4,375 units4,375 unitsBreak-even
volume (units)
In DollarsNew selling price 25$ Variable costs per unit (12) Contribution margin 13$
In DollarsPrevious units sold 4,375 Additional units sold 625 Expected sales volume 5,000
Anticipated changes:
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Decrease in Sales Price with an Increase in Sales Volume
IncomeUnits sold 4,375 Revenue @ $28 122,500$ Variable Expenses @ $12 (52,500) Contribution Margin @$16 70,000 Fixed Expenses (30,000) Net Income 40,000$
Current Situation
IncomeUnits sold 5,000 Revenue @ $25 125,000$ Variable Expenses @ $12 (60,000) Contribution Margin @$13 65,000 Fixed Expenses (30,000) Net Income 35,000$
Proposed Situation
Because Because budgeted income budgeted income will fall by $5,000, will fall by $5,000,
the proposal the proposal should be should be rejected!rejected!
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Increase in Fixed Costs and Increase in Sales Volume
After the previous project was rejected, the advertising manager believes that buying an additional $12,000 in
advertising can increase sales volume to 6,000 units. The contribution margin will remain at $16. Should the
company buy the additional advertising?
IncomeUnits sold 4,375 Revenue @ $28 122,500$ Variable Expenses @ $12 (52,500) Contribution Margin @$16 70,000 Fixed Expenses (30,000) Net Income 40,000$
Current SituationIncome
Units sold 6,000 Revenue @ $28 168,000$ Variable Expenses @ $12 (72,000) Contribution Margin @$16 96,000 Fixed Expenses (42,000) Net Income 54,000$
Proposed Situation
Profit = Contribution margin Profit = Contribution margin – Fixed cost– Fixed cost
Profit = (6,000 Profit = (6,000 × $16)× $16) – $42,000 =– $42,000 = $54,000$54,000
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Change in Several Variables
Management has been able to reduce variable Management has been able to reduce variable costs to $8 per bottle and decides to reduce costs to $8 per bottle and decides to reduce
the selling price per bottle to $25 (so the the selling price per bottle to $25 (so the contribution margin is now $17). Further, contribution margin is now $17). Further,
management believes that if advertising is cut management believes that if advertising is cut to $22,000, the company can still expect sales to $22,000, the company can still expect sales
volume to be 4,200 units.volume to be 4,200 units.
Should management adopt this plan?Should management adopt this plan?
Management has been able to reduce variable Management has been able to reduce variable costs to $8 per bottle and decides to reduce costs to $8 per bottle and decides to reduce
the selling price per bottle to $25 (so the the selling price per bottle to $25 (so the contribution margin is now $17). Further, contribution margin is now $17). Further,
management believes that if advertising is cut management believes that if advertising is cut to $22,000, the company can still expect sales to $22,000, the company can still expect sales
volume to be 4,200 units.volume to be 4,200 units.
Should management adopt this plan?Should management adopt this plan?
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Change in Several Variables
Profit = Contribution margin Profit = Contribution margin – Fixed – Fixed costcostProfit = (4,200 Profit = (4,200 × $17)× $17) – $22,000 =– $22,000 = $49,400$49,400
IncomeUnits sold 4,375 Revenue @ $28 122,500$ Variable Expenses @ $12 (52,500) Contribution Margin @$16 70,000 Fixed Expenses (30,000) Net Income 40,000$
Current SituationIncome
Units sold 4,200 Revenue @ $25 105,000$ Variable Expenses @ $8 (33,600) Contribution Margin @$17 71,400 Fixed Expenses (22,000) Net Income 49,400$
Proposed Situation
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Learning Objective
LO7LO7
To use the contribution margin ratio and the equation method to
conduct cost-volume-profit analysis
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Contribution Margin Ratio
The contribution margin ratio is the contribution margin divided by sales, computed using either total figures or per unit figures. Here is the total
dollar, per unit and contribution margin (CM) ratio for Bright Day when sales volume is 5,000
bottles.
Total Per Unit
CM Ratio
Revenue 180,000$ 36$ 100.00%Variable Expenses (120,000) 24 66.67%Contribution Margin 60,000 12$ 33.33%
Fixed Expenses (60,000) Net Income -$
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Contribution Margin RatioBright Day is considering the introduction of a
new product called Multi Minerals. Here is some per unit information about Multi
Minerals:
Bright Day expects to incur $24,000 in fixed marketing costs in connection with Multi Minerals.
Let’s look at the calculation of the break-even point in units and dollars.
Sales revenue per unit 20$ 100%Variable cost per unit 12 60%Contribution margin per unit 8$ 40%
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Contribution Margin Ratio
Break-even in Break-even in UnitsUnits
Break-even in Break-even in UnitsUnitsFixed costs
CM per unit
$24,000$8
= 3,000 units3,000 units
Break-even in Break-even in DollarsDollars
Break-even in Break-even in DollarsDollarsFixed costs
CM ratio$24,000
40%= $60,000$60,000
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Contribution Margin Ratio
Break-even in Break-even in UnitsUnits
Break-even in Break-even in UnitsUnits
Fixed costs + Desired profit
CM per unit
Break-even in Break-even in DollarsDollars
Break-even in Break-even in DollarsDollars
Fixed costs + Desired profit
CM ratioBright Day desires to earn a profit of $8,000 on Bright Day desires to earn a profit of $8,000 on
the sale of Multi Mineralsthe sale of Multi MineralsBright Day desires to earn a profit of $8,000 on Bright Day desires to earn a profit of $8,000 on
the sale of Multi Mineralsthe sale of Multi Minerals
= 4,000 units4,000 units$24,000 +
$8,000$8 $24,000 +
$8,00040%
= $80,000$80,000
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The Equation Method
At the break-even point:At the break-even point:
Sales = Variable cost + Fixed Sales = Variable cost + Fixed costcost
At the break-even point:At the break-even point:
Sales = Variable cost + Fixed Sales = Variable cost + Fixed costcost
Selling price per unit Variable cost per unit× = × + Fixed cost
Number of units sold Number of units sold
We can look at the above equation like this:We can look at the above equation like this:
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The Equation Method
Let’s use our information from Multi Minerals to solve the equation for the number of units sold.
20$ × Units = 12$ × Units + 24,000$ 8$ × Units =
Units =24,000$ 3,000
20$ × Units = 12$ × Units + 24,000$ 8$ × Units =
Units =24,000$ 3,000
If we want to consider the desired profit of $8,000 the solution would be:
20$ × Units = 12$ × Units + 32,000$ 8$ × Units =
Units =32,000$ 4,000
20$ × Units = 12$ × Units + 32,000$ 8$ × Units =
Units =32,000$ 4,000
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3-46
Check Yourself Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of
lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Use the profit in the coming month of $37,500. Use the equation method to determine how many equation method to determine how many lawnmowers Matrix must sell next month:lawnmowers Matrix must sell next month:
1.1. 3,000.3,000.
2.2. 3,500.3,500.
3.3. 4,000.4,000.
4.4. 4,500.4,500.
Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Use the profit in the coming month of $37,500. Use the equation method to determine how many equation method to determine how many lawnmowers Matrix must sell next month:lawnmowers Matrix must sell next month:
1.1. 3,000.3,000.
2.2. 3,500.3,500.
3.3. 4,000.4,000.
4.4. 4,500.4,500.
175$ × Units = 100$ × Units + 262,500$ 75$ × Units =
Units =262,500$
3,500
175$ × Units = 100$ × Units + 262,500$ 75$ × Units =
Units =262,500$
3,500
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End of Chapter 3