MEMORANDUM

DATE: April 13, 2011

TO: Ted Williams, President Williamson, Inc.

FROM: NAPZ Consulting Associates

Melissa Nicolay (Writer & Consultant), Isaac Posner (Excel & Consultant),

Symone Andrew (Editor & Consultant), Yue Zhang (Publisher & Consultant)

RE: Plan to Maximize Contribution Margin

We appreciate the opportunity to work with your company. As requested, our consulting group has devised a plan to improve the efficiency of operations for Williamson, Inc.

Based on our analysis, we have reached the following conclusions regarding the production of products X, Y, and Z:

1. The recommended amount(s) of each product to be produced is 0 X, 85 Y, and 330 Z.2. The total amount of labor hours needed to product these quantities would be 1000 hours.3. To produce each product, 335 pounds of Material A and 660 pounds of Material B will be

needed.

The remainder of this memo describes the basis for the conclusions reached during our analysis.

Product Cost and Profit Analysis

We began our analysis by determining the individual cost of producing each product based on the amount and cost of materials and labor required. As shown on Table 1, the individual vari-able cost for producing products X, Y, and Z are $52, $40, and $26, respectively. By subtracting the costs from their respective selling prices, it is clear that product Y yields the greatest contri-bution margin with $75, followed by product X with $70 and Z with $50.

Based on these numbers, it would appear that product Y—or even X—would be the more ideal choice to produce the highest quantity of, rather than product Z. However, as mentioned previ-ously, that is not the case for this specific situation. The determining factor here is the budget constraint of $11,980. For example, if we were to switch our conclusion values for Y and Z and produce 330 Y and 85 Z, this would create nearly $7,000 more profit than our model, but it would also be $4000 over the budget.

With these ideas in mind, we designed our Linear Programming Model to maximize the potential revenue while staying within the budget and meeting the weekly demand for product Y. The dif-ference between the maximum revenue and minimum cost will yield the highest possible contri-bution margin.

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Williamson Inc. Case StudyBudget $ 11,980.00    Product Types    X Y Z  Quantity 0 85 330             Selling Price $ 122.00 $ 115.00 $ 76.00  Cost Per Prod-uct $ 52.00 $ 40.00 $ 26.00    TotalRevenue $ - $ 9,775.00 $ 25,080.00 $ 34,855.00Total Cost $ - $ 3,400.00 $ 8,580.00 $ 11,980.00Profit $ - $ 6,375.00 $ 16,500.00 $ 22,875.00             X Y Z Cost Total UsageMaterial A 2 2 0.5 $ 4.00 335Material B 1 0 2 $ 4.00 660Labor Hours 5 4 2 $ 8.00 1000     Demand 0 85 0    

Table 1 | Product Production Analysis & Solution

Conclusions and Recommendations

We strongly believe that our plan to maximize contribution margins is the best possible solution for Williamson, Inc. given the current budget and demand. As previously stated, only 85 Y and 330 Z should be produced, using a total of 335 pounds of Material A, 660 pounds of Material B, and 1000 labor hours. Any other combination of products produced will result in a lower profit or costs that exceed your proposed budget. However, should there be any changes to the budget, demand, or other variables, please contact us to re-evaluate these amounts.

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Linear Programming Model

Maximize Z = 122X1 + 115X2 + 76X3

Subject to: X2 ≥ 8552X1 + 40X2 + 26X3 ≤ 11980X1, X2, X3 ≥ 0

Answer Report

Microsoft Excel 12.0 Answer Re-portWorksheet: [Copy of Copy of Williamson.xlsx]Sheet1Report Created: 4/13/2011 2:38:05 PM

Target Cell (Max)

Cell NameOriginal Value Final Value

$F$11 Revenue Total $ -

$ 34,855.00

Adjustable Cells

Cell NameOriginal Value Final Value

$B$6 Quantity X 0 0$C$6 Quantity Y 0 85$D$6 Quantity Z 0 330

ConstraintsCell Name Cell Value Formula Status Slack

$F$12Total Cost To-tal

$ 11,980.00

$F$12<=$B$2 Binding 0

$C$6 Quantity Y 85$C$6>=$C$20 Binding 0

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