For Problems 1-3 below, submit a non-technical consulting report (approximately ½ a page for each problem) accompanying by a technical appendix. The report should highlight your findings (e.g. business implications) and be prepared as if to be presented to an audience that has little knowledge of quantitative models. The technical appendix should include a formulation of a linear model, as we did in class (decisions, objective, constraints), and standard printouts of the spreadsheet model with an optimal solution (see Instructions for Standard Printouts below). Problem 1: Perfume (30 marks)
Rylon Corporation manufactures Brute and Chanelle perfumes. Raw material costs $3 per pound. Processing a pound of raw material takes one hour of laboratory time, and yields 3 ounces of Regular Brute and 4 ounces of Regular Chanelle perfume.
Regular Brute can be sold for $7/ounce and Regular Chanelle can be sold for $6/ounce. Rylon has the option of further processing Regular Brute perfume to produce Luxury Brute perfume, selling for $18/ounce. Each ounce of Regular Brute processed requires additional 3 hours of laboratory time and yields one ounce of Luxury Brute at a cost of $4. They can also process Regular Chanelle into Luxury Chanelle. Processing an ounce of Regular Chanelle requires 2 additional hours of lab time and yields one ounce of Luxury Chanelle, again at a cost $4. Luxury Chanelle sells for $14/ounce.
Rylon has 4000 pounds of raw material on hand, and 6000 hours of lab time available. How can they maximize their profit?
SKOLKOVO FT MBA
Problem 2: Production & advertisement (35 marks)
Your firm makes fluorescent paint pigments in four plants and ships them to four distributors (abbreviated "D1" through "D4"), as follows:
Unit Shipping Cost To
Capacity Unit Cost Impurities D1
$ 12.40 12
$ 11.55 15
$ 10.85 18
$ 12.05 12
The distributors' demand for the pigments is as follows:
Advertising Sensitivity 0.05
For example, distributor D1 will accept up to 700 units of pigment, plus 0.05 units for every dollar you spend on national advertising. Advertising is not separated by distributor: a single expenditure affects all distributors simultaneously. Thus, if you spend $100 on advertising, D1's demand will be 700 + (0.05)(100) = 705 units, D2's demand will be 600 + (0.1)(100) = 610 units, D3's demand will be 555 units, and D4's demand will be 687.5 units.
"Max impurities" indicates the maximum average impurity level allowed for shipments to each distributor. For instance, the shipments from the four plants to D1, when mixed together, should have an average impurity level of at most 15.0.
You have at most $59,000 to spend on production, shipping and advertising, and all the distributors pay you $28.50 per unit. How can you maximize your profits?
Note: this problem combines blending, transportation, and elements of the "pickles" problem. 1)
Formulate a linear model. Give clear definitions to your decision variables. Set up a spreadsheet model. Use Solver to find the optimal solution.
SKOLKOVO FT MBA
Problem 3: Kingston Manufacturing (35 marks)
Kingston Manufacturing produces heads for engines used in the manufacture of trucks. The production line is highly complex and measures 500 meters in length. Two types of engine heads are produced on the line: the P-Head and the H-Head. The P-Head is used in heavy duty trucks and the H-head is used in smaller trucks. Because only one type of head can be produced at a time, the line is either set up to manufacture the P-Head or the H-Head, but not both. Changeovers from producing one type to the other are made on weekends and cost...
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