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Table of ContentsChapter 1 (Introduction)

Special Products Break-Even Analysis (Section 1.2) 1.2 – 1.7

Power Notebooks Make or Buy Example 1.8This slide provides an example of a make or buy decision, where modeling can be illustrated. This would lead into a discussion about developing a model, culminating in either a spreadsheet model, an algebraic model, and/or a graph of the costs of the two alternatives.

Advertising Problem (UW Lecture) 1.9 – 1.22An illustration of the management science approach to a problem. At the University of Washington, this is the very first lecture in the core MBA class on management science. While it includes some advanced topics (Solver, nonlinear objectives, etc.) it can be taught entirely on the spreadsheet in a very intuitive way, and has proven to be a good introduction to the power of Solver. The next several lectures then would need to “back up” and cover more of the fundamentals of linear programming, modeling, the Solver, etc.

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Special Products Break-Even Analysis

• The Special Products Company produces expensive and unusual gifts.

• The latest new-product proposal is a limited edition grandfather clock.

• Data:– If they go ahead with this product, a fixed cost of $50,000 is incurred.

– The variable cost is $400 per clock produced.

– Each clock sold would generate $900 in revenue.

– A sales forecast will be obtained.

Question: Should they produce the clocks, and if so, how many?

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Expressing the Problem Mathematically

• Decision variable:– Q = Number of grandfather clocks to produce

• Costs:– Fixed Cost = $50,000 (if Q > 0)

– Variable Cost = $400 Q

– Total Cost =

• 0, if Q = 0

• $50,000 + $400 Q, if Q > 0

• Profit:– Profit = Total revenue – Total cost

• Profit = 0, if Q = 0

• Profit = $900Q – ($50,000 + $400Q) = –$50,000 + $500Q, if Q > 0

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Analysis of the Problem

$

$40,000

$80,000

$120,000

$160,000

$200,000

0 40 80 120 160 200

Revenue = $900 x

Fixed cost

Loss

Profit

Cost = $50,000 + $400 x

x

Break-even point = 100 units

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Management Science Interactive Modules

• Sensitivity analysis can be performed using the Break-Even module in the Interactive Management Science Modules (available on your MS Courseware CD packaged with the text).

– Here we see the impact of changing the fixed cost to $75,000.

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Special Products Co. Spreadsheet

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B C D E FData Results

Unit Revenue $900 Total Revenue $270,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $120,000Sales Forecast 300 Profit (Loss) $100,000

Production Quantity 300

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E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Range Name CellFixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

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Special Products Co. Spreadsheet

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B C D E FData Results

Unit Revenue $900 Total Revenue $270,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $120,000Sales Forecast 300 Profit (Loss) $100,000

Production Quantity 300 Break-Even Point 100

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E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Break-Even Point =FixedCost/(UnitRevenue-MarginalCost)

Range Name CellBreakEvenPoint F9FixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

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Make or Buy?

• Power Notebooks, Inc. is a manufacturer of notebook computers. They are trying to decide whether to purchase the LCD screens for their computers from an outside supplier or to manufacture the screens in-house.

• The screens cost $100 each from the outside supplier.

• To set up the assembly process required to produce the screens in-house would cost $10,000. They could then produce each screen for $75.

Question: For what range of production volume is each alternative best?

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An Advertising Problem

• Parker Mothers is a manufacturer of children’s toys and games. One of their hottest selling toys is an interactive electronic Harry Potter doll.

• Some data:– Unit Variable Cost: $48– Unit Selling Price: $65– Sales Force Salary: $9,000– Fixed Overhead: $23,000

• Parker Mothers has analyzed past data for the Harry Potter doll (and other similar toys), and determined that sales are affected by a number of factors:

– the season (e.g., more at Christmas, more when a new Harry Potter book or movie is released, etc.),

– the size of the sales force devoted to the product,– the level of advertising.

Question: What should the advertising budget for the Harry Potter doll be? (Proposal: $10,000)

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Predicting the Sales Level

• After performing a statistical regression analysis, they estimate that sales for the quarter will be approximately related to the season, sales force salary, and advertising budget, as follows:

• Seasonality Factors:– Q1: 1.2 (publication of new Harry Potter book)– Q2: 0.7– Q3: 0.8– Q4: 1.3 (Christmas and expected release of new Harry Potter movie)

• Effect of Advertising / Sales Force:

Sales(35)(Seasonality Factor) Advertising+

Sales Force2

Advertising + (Sales Force/2)

Sales

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Spreadsheet for Quarter 1

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B CParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2

Decision Variable:Advertising $10,000

Quarter Q1Units Sold 5057

Sales Revenue $328,736 Cost of Sales $242,759Gross Margin $85,977

Advertising Cost $10,000Total Fixed Costs $32,000

Profit $43,977

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B CQuarter Q1

Units Sold =35*C8*SQRT(C11+($C$6/2))

Sales Revenue =C14*$C$5 Cost of Sales =C14*$C$4Gross Margin =C16-C17

Advertising Cost =C11Total Fixed Costs =$C$6+$C$7

Profit =C18-C20-C21

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Trial Solutions

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B C D E F G HParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2

Decision Variable:Advertising $10,000 $40,000 $70,000 $100,000 $130,000 $160,000

Quarter Q1 Q1 Q1 Q1 Q1 Q1Units Sold 5057 8860 11464 13577 15403 17035

Sales Revenue $328,736 $575,894 $745,145 $882,512 $1,001,207 $1,107,250 Cost of Sales $242,759 $425,276 $550,261 $651,701 $739,353 $817,661Gross Margin $85,977 $150,618 $194,884 $230,811 $261,854 $289,588

Advertising Cost $10,000 $40,000 $70,000 $100,000 $130,000 $160,000Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $32,000 $32,000

Profit $43,977 $78,618 $92,884 $98,811 $99,854 $97,588

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The Excel Solver

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B CParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2

Decision Variable:Advertising $10,000

Quarter Q1Units Sold 5057

Sales Revenue $328,736 Cost of Sales $242,759Gross Margin $85,977

Advertising Cost $10,000Total Fixed Costs $32,000

Profit $43,977

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The Optimized Solution

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B CParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2

Decision Variable:Advertising $122,949

Quarter Q1Units Sold 14994

Sales Revenue $974,610 Cost of Sales $719,712Gross Margin $254,898

Advertising Cost $122,949Total Fixed Costs $32,000

Profit $99,949

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Four Quarters Spreadsheet

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B C D E F GParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $10,000 $10,000 $10,000 $10,000 $40,000

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 5057 2950 3372 5479 16858

Sales Revenue $328,736 $191,762 $219,157 $356,130 $1,095,785 Cost of Sales $242,759 $141,609 $161,839 $262,988 $809,195Gross Margin $85,977 $50,153 $57,318 $93,142 $286,590

Advertising Cost $10,000 $10,000 $10,000 $10,000 $40,000Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $43,977 $8,153 $15,318 $51,142 $118,590

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Four Quarters Solver Optimized

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B C D E F GParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $122,949 $38,868 $52,144 $145,076 $359,036

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 14994 5102 6664 17597 44357

Sales Revenue $974,610 $331,638 $433,160 $1,143,813 $2,883,221 Cost of Sales $719,712 $244,902 $319,872 $844,662 $2,129,148Gross Margin $254,898 $86,736 $113,288 $299,151 $754,073

Advertising Cost $122,949 $38,868 $52,144 $145,076 $359,036Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $99,949 $15,868 $29,144 $122,076 $267,037

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Residual Effect

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B C D E F GParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $24,077 $0 $12,575 $11,348 $48,000

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 7100 2742 3659 6441 19942

Sales Revenue $461,503 $178,231 $237,821 $418,664 $1,296,219 Cost of Sales $340,802 $131,617 $175,622 $309,167 $957,208Gross Margin $120,701 $46,614 $62,199 $109,497 $339,011

Advertising Cost $24,077 $0 $12,575 $11,348 $48,000Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $64,623 $14,614 $17,624 $66,149 $163,011

1415

B C DQuarter Q1 Q2

Units Sold =35*C8*SQRT(C12+($C$6/2)) =35*D8*SQRT(D12+(C12/3)+($C$6/2))

1415

E F GQ3 Q4 Total

=35*E8*SQRT(E12+(D12/3)+($C$6/2)) =35*F8*SQRT(F12+(E12/3)+($C$6/2)) =SUM(C15:F15)

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Residual Effect (Solver Optimized)

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B C D E F GParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $227,776 -$8,735 $125,861 $103,122 $448,023

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 20242 6560 9996 17597 54395

Sales Revenue $1,315,723 $426,392 $649,740 $1,143,813 $3,535,668 Cost of Sales $971,611 $314,874 $479,808 $844,662 $2,610,955Gross Margin $344,112 $111,518 $169,932 $299,151 $924,713

Advertising $227,776 -$8,735 $125,861 $103,122 $448,023Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $84,337 $88,253 $12,071 $164,029 $348,690

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Solver Options

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Residual Effect (Solver Re-Optimized)

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B C D E F GParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $221,033 $0 $122,949 $104,093 $448,075

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 19946 6850 9996 17597 54389

Sales Revenue $1,296,487 $445,268 $649,740 $1,143,813 $3,535,307 Cost of Sales $957,406 $328,813 $479,808 $844,662 $2,610,688Gross Margin $339,081 $116,455 $169,932 $299,151 $924,619

Advertising Cost $221,033 $0 $122,949 $104,093 $448,075Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $86,048 $84,455 $14,983 $163,059 $348,544

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Residual Effect with Budget (Optimized)

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B C D E F G H IParameters:Unit Variable Cost $48Unit Price $65Salesforce Salary $9,000Fixed Overhead $23,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: Advertising BudgetAdvertising $24,077 $0 $12,575 $11,348 $48,000 <= $48,000

Quarter Q1 Q2 Q3 Q4 TotalUnits Sold 7100 2742 3659 6441 19942

Sales Revenue $461,503 $178,231 $237,821 $418,664 $1,296,219 Cost of Sales $340,802 $131,617 $175,622 $309,167 $957,208Gross Margin $120,701 $46,614 $62,199 $109,497 $339,011

Advertising Cost $24,077 $0 $12,575 $11,348 $48,000Total Fixed Costs $32,000 $32,000 $32,000 $32,000 $128,000

Profit $64,623 $14,614 $17,624 $66,149 $163,011

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Adding a Constraint in Solver