McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2008 1.1 Table of Contents Chapter 1...

© The McGraw-Hill Companies, Inc., 2008

1.1McGraw-Hill/Irwin

Table of ContentsChapter 1 (Introduction)

Special Products Break-Even Analysis (Section 1.2)

1.2 – 1.6

Advertising Problem (UW Lecture)

1.8 – 1.21An 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.



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?



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



Special Products Co. Spreadsheet

34567

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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B C D E FData Results

Unit Revenue $900 Total Revenue $180,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $80,000Sales Forecast 300 Profit (Loss) $50,000

Production Quantity 200



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



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.



Special Products Co. Spreadsheet

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

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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

3456789

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)



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

– Fixed Overhead: $42,000

• 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: $50,000)



Predicting the Sales Level

• After performing a statistical regression analysis, they estimate that sales for the quarter will be approximately related to the season 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:

Advertising + (Sales Force/2)

Sales

Sales (Seasonality Factor) 2000+35 $Advertising



Spreadsheet for Quarter 1

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B CParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2

Decision Variable:Advertising $50,000

Quarter Q1Expected Units Sold 11,791

Sales Revenue $766,447 Cost of Sales $565,991Gross Margin $200,455

Advertising Cost $50,000Fixed Overhead $42,000

Profit $108,455

1213141516171819202122

B CQuarter Q1

Expected Units Sold =C7*(2000+35*SQRT(C10))

Sales Revenue =C13*$C$5 Cost of Sales =C13*$C$4Gross Margin =C15-C16

Advertising Cost =C10Fixed Overhead =$C$6

Profit =C17-C19-C20



Trial Solutions345678910111213141516171819202122






Profit $108,455

10111213141516171819202122

C$100,000

Q115,682

$1,019,302$752,715$266,587

$100,000$42,000

$124,587

10111213141516171819202122

C$150,000

Q118,667

$1,213,324$895,993$317,331

$150,000$42,000

$125,331

10111213141516171819202122

C$200,000

Q121,183

$1,376,893$1,016,783$360,111

$200,000$42,000

$118,111

910111213141516171819202122

B CDecision Variable:Advertising $125,000


Sales Revenue $1,121,201 Cost of Sales $827,964Gross Margin $293,237


Profit $126,237



The Excel Solver

345678910111213141516171819202122






Profit $108,455



The Optimized Solution

345678910111213141516171819202122




Sales Revenue $1,130,610 Cost of Sales $834,912Gross Margin $295,698


Profit $126,249



Four Quarters Spreadsheet

34567891011121314151617181920212223

B C D E F GParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2 0.7 0.8 1.3

TotalDecision Variables: AdvertisingAdvertising $50,000 $50,000 $50,000 $50,000 $200,000

Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 11,791 6,878 7,861 12,774 39,305

Sales Revenue $766,447 $447,094 $510,964 $830,317 $2,554,822 Cost of Sales $565,991 $330,162 $377,328 $613,157 $1,886,638Gross Margin $200,455 $116,932 $133,637 $217,160 $668,184

Advertising Cost $50,000 $50,000 $50,000 $50,000 $200,000Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000

Profit $108,455 $24,932 $41,637 $125,160 $300,184



Four Quarters Solver Optimized

34567891011121314151617181920212223

B C D E F GParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2 0.7 0.8 1.3



Sales Revenue $1,130,610 $422,638 $537,160 $1,312,813 $3,403,221 Cost of Sales $834,912 $312,102 $396,672 $969,462 $2,513,148Gross Margin $295,698 $110,536 $140,488 $343,351 $890,073


Profit $126,249 $25,168 $41,844 $151,776 $345,037



Residual Effect

34567891011121314151617181920212223

B C D E F GParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2 0.7 0.8 1.3Advertising Previous Q4 $50,000



Sales Revenue $1,037,305 $508,078 $521,654 $1,200,723 $3,267,760 Cost of Sales $766,010 $375,196 $385,221 $886,688 $2,413,115Gross Margin $271,295 $132,882 $136,433 $314,035 $854,645


Profit $101,846 $47,514 $37,789 $122,460 $309,608

781314

B C DSeasonality 1.2 0.7Advertising Previous Q4 50000

Quarter Q1 Q2Expected Units Sold =C7*(2000+35*SQRT(0.7*C11+0.3*C8)) =D7*(2000+35*SQRT(0.7*D11+0.3*C11))

1314

E F GQ3 Q4 Total

=E7*(2000+35*SQRT(0.7*E11+0.3*D11)) =F7*(2000+35*SQRT(0.7*F11+0.3*E11)) =SUM(C14:F14)



Residual Effect (Solver Optimized)

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TotalDecision Variables: AdvertisingAdvertising $173,577 -$21,148 $130,494 $48,777 $331,700


Sales Revenue $1,164,637 $398,437 $634,621 $969,669 $3,167,364 Cost of Sales $860,040 $294,231 $468,643 $716,063 $2,338,977Gross Margin $304,597 $104,207 $165,978 $253,606 $828,388

Advertising Cost $173,577 -$21,148 $130,494 $48,777 $331,700Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000

Profit $89,021 $83,354 -$6,516 $162,829 $328,688



Solver Options



Residual Effect (Solver Re-Optimized)

34567891011121314151617181920212223


TotalDecision Variables: AdvertisingAdvertising $155,280 $0 $121,431 $52,661 $329,371


Sales Revenue $1,116,152 $434,714 $634,621 $969,669 $3,155,157 Cost of Sales $824,236 $321,020 $468,643 $716,063 $2,329,962Gross Margin $291,917 $113,694 $165,978 $253,606 $825,195

Advertising Cost $155,280 $0 $121,431 $52,661 $329,371Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000

Profit $94,637 $71,694 $2,547 $158,945 $327,823



Residual Effect with Budget (Optimized)

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B C D E F G H IParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2 0.7 0.8 1.3Advertising Previous Q4 $50,000

TotalDecision Variables: AdvertisingAdvertising $91,433 $0 $75,727 $32,841 $200,000 <= $200,000


Sales Revenue $923,334 $354,749 $523,030 $801,286 $2,602,398 Cost of Sales $681,846 $261,969 $386,237 $591,719 $1,921,771Gross Margin $241,487 $92,781 $136,792 $209,567 $680,627

Advertising Cost $91,433 $0 $75,727 $32,841 $200,000Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000

Profit $108,055 $50,781 $19,066 $134,726 $312,627



Adding a Constraint in Solver

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