© 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.
© The McGraw-Hill Companies, Inc., 2008
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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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1.4McGraw-Hill/Irwin
Special Products Co. Spreadsheet
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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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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
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1.5McGraw-Hill/Irwin
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
© The McGraw-Hill Companies, Inc., 2008
1.6McGraw-Hill/Irwin
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.
© The McGraw-Hill Companies, Inc., 2008
1.7McGraw-Hill/Irwin
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
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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)
© The McGraw-Hill Companies, Inc., 2008
1.8McGraw-Hill/Irwin
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)
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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 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
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1.10McGraw-Hill/Irwin
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
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1.11McGraw-Hill/Irwin
Trial Solutions345678910111213141516171819202122
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
10111213141516171819202122
C$100,000
Q115,682
$1,019,302$752,715$266,587
$100,000$42,000
$124,587
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C$150,000
Q118,667
$1,213,324$895,993$317,331
$150,000$42,000
$125,331
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C$200,000
Q121,183
$1,376,893$1,016,783$360,111
$200,000$42,000
$118,111
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B CDecision Variable:Advertising $125,000
Quarter Q1Expected Units Sold 17,249
Sales Revenue $1,121,201 Cost of Sales $827,964Gross Margin $293,237
Advertising Cost $125,000Fixed Overhead $42,000
Profit $126,237
© The McGraw-Hill Companies, Inc., 2008
1.12McGraw-Hill/Irwin
The Excel Solver
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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
© The McGraw-Hill Companies, Inc., 2008
1.13McGraw-Hill/Irwin
The Optimized Solution
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B CParameters:Unit Variable Cost $48Unit Price $65Fixed Overhead $42,000Seasonality 1.2
Decision Variable:Advertising $127,449
Quarter Q1Expected Units Sold 17,394
Sales Revenue $1,130,610 Cost of Sales $834,912Gross Margin $295,698
Advertising Cost $127,449Fixed Overhead $42,000
Profit $126,249
© The McGraw-Hill Companies, Inc., 2008
1.14McGraw-Hill/Irwin
Four Quarters Spreadsheet
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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
© The McGraw-Hill Companies, Inc., 2008
1.15McGraw-Hill/Irwin
Four Quarters Solver Optimized
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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 $127,449 $43,368 $56,644 $149,576 $377,036
Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 17,394 6,502 8,264 20,197 52,357
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
Advertising Cost $127,449 $43,368 $56,644 $149,576 $377,036Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000
Profit $126,249 $25,168 $41,844 $151,776 $345,037
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Residual Effect
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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
TotalDecision Variables: AdvertisingAdvertising $127,449 $43,368 $56,644 $149,576 $377,036
Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 15,959 7,817 8,025 18,473 50,273
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
Advertising Cost $127,449 $43,368 $56,644 $149,576 $377,036Fixed Overhead $42,000 $42,000 $42,000 $42,000 $168,000
Profit $101,846 $47,514 $37,789 $122,460 $309,608
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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)
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Residual Effect (Solver Optimized)
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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
TotalDecision Variables: AdvertisingAdvertising $173,577 -$21,148 $130,494 $48,777 $331,700
Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 17,917 6,130 9,763 14,918 48,729
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
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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 $65Fixed Overhead $42,000Seasonality 1.2 0.7 0.8 1.3Advertising Previous Q4 $50,000
TotalDecision Variables: AdvertisingAdvertising $155,280 $0 $121,431 $52,661 $329,371
Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 17,172 6,688 9,763 14,918 48,541
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
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1.20McGraw-Hill/Irwin
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
Quarter Q1 Q2 Q3 Q4 TotalExpected Units Sold 14,205 5,458 8,047 12,327 40,037
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
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1.21McGraw-Hill/Irwin
Adding a Constraint in Solver
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