| Course | BU 407 Quantitative Decision-Making |
|---|---|
| Unit | Unit 8 |
| Paper type | Quantitative recommendation file |
| Length | About 820 words, 5 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Analytics |
| Updated | September 2026 |
Free sample paper for BU 407 Unit 8
Buy the Extra Milk and Run the Cheese Vats on Saturday: A Quantitative Recommendation File for a Composite Dairy Plant Manager, With the Model Underneath
Student Name
Business, Herzing University
BU 407: Quantitative Decision-Making
Instructor Name
April 29, 2026
Buy the Extra Milk and Run the Cheese Vats on Saturday: A Quantitative Recommendation File for a Composite Dairy Plant Manager, With the Model Underneath
Memo
To: Plant Manager, Eau Claire plant, Northwoods Dairy Cooperative. From: Plant operations analyst. Date: April 29, 2026. Subject: Two changes that would add about $7,800 a week in contribution.
I recommend two changes to the Eau Claire plant's weekly operation, starting in May. First, accept the neighboring cooperative's offer of extra raw milk, but buy only 260 thousand pounds a week, not the full 400 thousand offered. Second, add a Saturday cheese vat shift of 40 vat hours a week.
Together, the two changes would raise weekly contribution by about $18,200 before their costs. The extra milk costs about $7,800 a week in premium, at $30 per thousand pounds above our standard price, and the Saturday shift costs about $2,600 a week in labor and utilities. The net gain is about $7,800 a week, or roughly $405,000 a year. Taken separately, the milk purchase would net about $4,900 a week and the Saturday shift about $2,900; the two do not interfere with each other at these levels, so doing both captures the full gain.
The reason to stop at 260 thousand pounds is that the packaging line becomes full at that point. Milk beyond 260 thousand pounds a week could not be turned into more product without more packaging hours, so it would add cost and no contribution. The Saturday shift works because the cheese vats are the tightest constraint on cheese output, and each added vat hour is worth about $137 in contribution even after accounting for the milk that cheese uses instead of fluid milk.
The main risk is that the extra fluid milk the plan produces, about 15 thousand gallons a week more than today, must find buyers at current prices. The grocery chain contract takes our current volume comfortably, but the sales team should confirm before the first delivery that the added volume can be sold without discounts.
If you approve both changes, I suggest a four-week trial before making them permanent. The trial would confirm three things the model assumes: that the neighboring cooperative can deliver 260 thousand pounds reliably each week, that the Saturday crew can run the vats at the same yield as weekday crews and that the added fluid milk sells at current prices. I will report the actual weekly contribution against the model's forecast at the end of the trial.
Assumptions Register
The register lists every input to the model with its source and whether it was given in the case, derived from other inputs or chosen by the analyst.
| Input | Value | Source | Type |
|---|---|---|---|
| Contribution per thousand gallons of fluid milk | $420 | Plant cost records | Given |
| Contribution per thousand cases of yogurt | $1,150 | Plant cost records | Given |
| Contribution per thousand lb of cheese | $900 | Plant cost records | Given |
| Raw milk use per unit (fluid, yogurt, cheese) | 8.6, 6.0, 10.0 thousand lb | Plant engineering | Given |
| Weekly raw milk supply | 2,400 thousand lb | Member deliveries | Given |
| Pasteurizer, packaging and vat hours | 300, 420, 120 per week | Plant schedule | Given |
| Yogurt demand ceiling | 90 thousand cases per week | Sales team estimate | Given |
| Fluid milk contract minimum | 120 thousand gallons per week | Grocery contract | Given |
| Premium on purchased milk | $30 per thousand lb | Neighboring cooperative's offer | Given |
| Saturday vat shift | 40 vat hours for $2,600 per week | Plant manager's estimate | Chosen |
| Constant contribution per unit at higher volume | Assumed | Analyst | Chosen |
Technical Appendix: The Model
The decision variables are weekly production of fluid milk in thousands of gallons, x1; yogurt in thousands of cases, x2; and cheese in thousands of pounds, x3. The objective is to maximize 420 x1 + 1,150 x2 + 900 x3. The six constraints, set out in full in the earlier model summary, limit raw milk to 2,400 thousand pounds, pasteurizer time to 300 hours, packaging time to 420 hours and cheese vat time to 120 hours a week, cap yogurt at 90 thousand cases and require at least 120 thousand gallons of fluid milk; all variables are nonnegative. Solved as it stands, the model's best weekly plan is roughly 169.8 (fluid), 90 (yogurt) and 40 (cheese), worth about $210,802 in contribution (Hillier & Lieberman, 2015).
Technical Appendix: The Sensitivity Pass
The sensitivity report gives a shadow price of $48.84 per thousand pounds of raw milk, which holds until 260 thousand added pounds, and $137.21 per cheese vat hour, which holds until 128.4 added hours. Both proposed changes fall within their ranges. Because shadow prices are valid only one change at a time, the combined change was checked by re-solving the model rather than by adding the two gains. The re-solves gave these results.
| Scenario | Fluid milk | Yogurt | Cheese | Weekly contribution | Gain before costs | Added cost | Net gain |
|---|---|---|---|---|---|---|---|
| Current plan | 169.8 | 90 | 40.0 | $210,802 | |||
| Buy 260 thousand lb milk | 200.0 | 90 | 40.0 | $223,500 | $12,698 | $7,800 | $4,898 |
| Add 40 vat hours | 154.3 | 90 | 53.3 | $216,291 | $5,488 | $2,600 | $2,888 |
| Both changes | 184.5 | 90 | 53.3 | $228,988 | $18,186 | $10,400 | $7,786 |
Reading the Model Against the Memo
The re-solves confirm the memo's figures and one detail the memo mentions only briefly: adding vat hours shifts milk from fluid milk to cheese, while buying milk adds fluid milk, so the combined plan produces about 184.5 thousand gallons of fluid milk, roughly 15 thousand gallons more than today. That is the volume the sales team must place. The yogurt ceiling stays binding in every scenario, which confirms the earlier finding that yogurt sales, not production, limit the plant's most profitable product. If the sales team could raise yogurt demand, each thousand additional cases would be worth about $857 a week, a larger opportunity than either change recommended here, and worth pursuing next. Render et al. (2018) recommend that model results be presented with their assumptions so that a manager can see which inputs drive the answer, which is the purpose of the register above. Northwoods Dairy Cooperative, its plant and every figure are composites created for this course (Winston, 2004).
References
Hillier, F. S., & Lieberman, G. J. (2015). Introduction to operations research (10th ed.). McGraw-Hill Education.
Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2018). Quantitative analysis for management (13th ed.). Pearson.
Winston, W. L. (2004). Operations research: Applications and algorithms (4th ed.). Thomson Brooks/Cole.
The Herzing BU 407 Unit 8 instructions
The final BU 407 assignment asks for a quantitative recommendation file combining a model with a short memo to a decision maker. Most versions want the memo first, stating the recommendation and a few supporting figures in business language, followed by an assumptions register and a technical appendix with the model, its solution and a sensitivity analysis. Many rubrics reward checking combined changes by re-solving rather than adding sensitivity figures. Instructors grade whether the memo and the technical work agree. A model from an earlier unit may be reused if extended. Expect a longer document with tables, citing quantitative methods sources in APA 7, and address the memo to a named role rather than to an instructor.
Inside the BU 407 Unit 8 example
The sample opens with a memo to the plant manager that states two changes, their combined and separate gains, the reason for the purchase limit, the main risk and a proposed trial. An assumptions register lists eleven inputs with values, sources and types. The technical appendix summarizes the model and current solution, then reports the sensitivity figures and a table of four re-solved scenarios showing production, contribution, costs and net gains. A final section reads the model against the memo, noting the added fluid milk volume the sales team must place and pointing to yogurt demand, worth about $857 per thousand cases, as the larger opportunity for future work.
BU 407 Unit 8 rubric: what full points look like
The rubric for the recommendation file typically weighs the memo, the assumptions register, the technical appendix and the consistency between them. The memo earns full points when it states the recommendation first with a few clear figures and names risks. The register is judged by complete inputs with sources and types. The appendix scores highest when it presents the model, the sensitivity analysis and verification of combined changes, as the sample's re-solve table does. Consistency rewards figures that match exactly between memo and appendix. Instructors also credit identifying further opportunities the model reveals and naming a trial that would test the recommendation before it becomes permanent. Professional formatting and citations complete the grade.
Common BU 407 Unit 8 mistakes, and how to avoid them
The most common Unit 8 mistake is leading with the model and burying the recommendation. Another is writing the memo in technical language a manager cannot use. Students often add shadow-price gains for two changes without re-solving, which can overstate or understate the combined effect. Some files omit the assumptions register, leaving the manager unable to see which inputs drive the answer. Others let figures in the memo drift from those in the appendix, which undermines trust in both. Finally, name the main risk and a way to test the recommendation before committing to it; a short trial with a report date makes approval easier for a cautious manager.
Get a BU 407 Unit 8 example written to your instructions
Send the Unit 8 instructions and the BU 407 rubric, plus the earlier model or data the file has to build on. We write a custom example that opens with the recommendation, keeps the technical work in an appendix, registers every assumption and states the threshold that would change the advice. First custom sample free, returned in 24 to 48 hours.
More BU 407 papers and business analytics samples
- BU 407 Unit 1: Payoff table write-up
- BU 407 Unit 2: Expected value comparison
- BU 407 Unit 3: Forecast selection record
- BU 407 Unit 4: Optimization model summary
- BU 407 Unit 5: Sensitivity table analysis
- BU 407 Unit 6: Transportation model record
- BU 407 Unit 7: Simulation output brief
- BU 351 Unit 8: End-to-end analytics case
- BU 455 Unit 8: Architecture recommendation
- BU 451 Unit 8: Reproducible analysis submission
- BU 453 Unit 8: Database design project
BU 407 Unit 8 questions, answered
How technical should the memo be?
Written for the role it names. A memo to an operations manager can use the vocabulary of the operation but should not require the reader to interpret solver output. Put every model detail in the appendix, and in the memo report only figures a decision turns on, each with its unit and its meaning stated in one clause.
Can I reuse the model from an earlier unit?
Most instructions expect it, and building forward is the point of a closing unit. Fix whatever the earlier submission lost points on instead of carrying that work through untouched, then reframe it around the question this file settles. Text that still answers its original prompt is what graders flag most often in an assembled submission.
What if the model contradicts what the manager expects?
Write the contradiction and then explain it. Say which assumption drives the difference, and name the input value at which the manager's expectation would be correct, since that is where a quantitative file earns its keep. A recommendation quietly adjusted to match expectation is worth less than an honest one naming the disagreement and its source.
Where can I find a free BU 407 Unit 8 sample paper?
The finished BU 407 Unit 8 file, memo through technical appendix, is posted above for free. If you need a recommendation file built on your own model, share the prompt and the model, and a free custom file can be put together for you, usually within two days.
How technical should the BU 407 Unit 8 memo be?
Not very. The sample's memo uses plain business terms and a handful of figures, while the model, sensitivity report and re-solves sit in the appendix. A manager should be able to act on the memo without reading the appendix.