Review Problems
1. Product Mix
Yamamoto Motorcycle Ltd. is planning next week’s production schedule. They manufacture two retro-style cruisers: the Pirate and the Buccaneer. Both machines are mechanically identical, but the Pirate includes additional chrome trim. Each Pirate requires 4 kg of chrome while the Buccaneer consumes only 3 kg. Yamamoto’s chrome inventory is limited to 480 kg for the upcoming week. All other resources (labor, components, etc.) are plentiful. Direct costs for the motorcycles, converted from yen to dollars, are $3200 for the Pirate and $3000 for the Buccaneer. Prices (fob factory) are $6000 and $5000, respectively. Yamamoto must honor a previous contract with the California Cruiser Club to deliver 10 Pirates and 20 Buccaneers from next week’s production run. In addition, marketing forecasts indicate an open-market demand of 70 Pirates and 80 Buccaneers for the coming week.
a) Define Yamamoto’s production problem for LP model formulation purposes.
b) Formally define management’s decision variables.
c) Formulate the LP model algebraically.
d) Convert the model to its standard form.
e) Formally define the model’s slack and surplus variables.
f) Graph the model and determine the feasible region.
g) Use the isoprofit/isocost-line method to determine the optimal solution and value:
• from a revenue-generation standpoint
• from a strict cost-reduction standpoint
• from a contribution-to-profit standpoint
h) Determine the binding and nonbinding constraints for each of the solutions in (g).
i) Create an Excel spreadsheet model for Yamamoto’s problem.
j) Solve the model with Solver and obtain the Answer Reports for each of the standpoints given in (g). Also obtain the Sensitivity Report for the contribution-to-profit model.
k) Verify (g) and (h) from the Answer Reports.
Refer to the contribution-to-profit reports for the following items:
l) Should Yamamoto purchase additional kilograms of chrome on the spot market if they are offered at $100/kg over and above the usual price paid by Yamamoto? At that price, how much extra chrome should Yamamoto buy, if any? Determine the new profit contribution if any extra chrome is purchased.
m) Explain the effects on the optimal solution (of the original profit model) if direct costs for the Buccaneer are reduced by $100 per unit, all else remaining unchanged.
n) Yamamoto’s sales manager is confident they can sell an additional 20 Pirates if the company incurs an additional sales expense of $1000. Should Yamamoto do so? Why?
o) Yamamoto is considering implementing a new policy. To enhance its image of exclusivity, the number of Pirates produced would not exceed half the production of Buccaneers. Modify the original model and determine if this policy is warranted from a profit standpoint. If it is not warranted, what else could be done to make the new policy feasible?
Yamamoto Motorcycle presents:
Pirates of the Caribbean
The Historical Yamamoto: A Question of Strategy
El Almirante Isoroku Yamamoto
Pearl Harbor
A Question of Honor (scenes from "Tora Tora Tora")
A Question of Honor (scenes from "Pearl Harbor")
America Reacts
Midway
How Adm. Yamamoto Was Assassinated
Death of Adm. Isoroku Yamamoto
The Bombs
Hiroshima
Hiroshima & Nagasaki
2. Blending & Product Mix
Café Café SA blends and markets three premium coffee products (Espresso, Cremosso and Spumosso) from the finest imported coffee beans. Each brand is sold in 4-ounce and 8-ounce tins (cans) that are placed inside handsome miniature burlap sacks (see photo). Café Café’s secret recipes (which they trust you will not divulge) make use of select Angolan, Brazilian and Colombian beans in the following proportions:
Coffee beans are purchased in 50-pound sacks. The beans are then roasted and ground following special Costa Rican procedures using two types of Italian machines: roasters and grinders. To obtain the characteristic flavor, aroma and consistency of each particular brand, roasting must be done at different temperatures and conditions for the following time periods per hundredweight (100-pound batch): Espresso: 45 minutes; Cremosso: 30 minutes; Spumosso: 20 minutes. Grinding takes 20 minutes per hundredweight for the Espresso and 15 minutes for the other two brands. Packing consumes 10 minutes per hundredweight for all brands. Available machine times for the upcoming week are 160 hours for roasters and 120 hours for grinders. Packing machine hours are essentially unlimited.
Marketing forecasts for the upcoming week call for the following maximum and minimum demands:
Café Café, of course, is interested in meeting minimum demands but not exceeding the maximum forecasts since product freshness is critical. Selling prices for the products are as follows:
Coffee bean prices, per 50-pound sack, are $95 for Angolan, $110 for Brazilian, and $120 for Colombian. Availability is unlimited except for Brazilian, which due to poor harvests because of cold weather is currently restricted to 4,000 pounds per week. The company considers all other production-related expenses as sunk costs. Determine Café Café’s optimal production plan for the upcoming week and its total contribution to profit.
The Art of Café Café
3. Marketing — Advertising Strategy
Gecko Inc. relies almost exclusively on advertisement to attract new customers to its Website, where its auto insurance policies are sold. Ads can be placed in broadcast TV, cable TV, print media (newspapers, magazines), highway billboards, and airport display panels. All TV commercials are 30 second spots; the other ads are static images of colorful posters. Gecko measures the reach of its ads as a percentage of the total number of persons in a target geographical market that will be exposed to at least one ad during the campaign. Market research shows that the media used by Gecko yield the following reach points (percentages); costs per ad are also included:
Gecko’s advertising budget for their next campaign totals $100 million. Marketing strategy dictates that at least 30% of the budget must be allocated to each of the TV media and at least 5% to each of the remaining media. In addition, airport ads are not to exceed 5000 display panels in total. Determine how Gecko should allocate its advertising budget in order to maximize aggregate reach points. (By the way, if you think this problem is messy, I've got good news — I just saved a bunch of money on car insurance by switching to Gecko.) 
Gecko presents:
GEICO caveman commercial
4. Sensitivity Analysis
For the Phantom of the Opera problem, answer the following:
a) Determine the solution and value of the problem if the profit margin of the full-face masks doubles.
b) Explain what would need to be done if the profit margin of the half-face masks doubles.
c) Which is the Phantom's most important resource? Why?
d) Explain why there is no limit to the allowable RHS increases for the nonbinding resources.
BRIEF ANSWERS TO PROBLEMS
Phantom: FF = 300, HF = 200, P* = $2200
Pastry Chefs: SG = 5, SOB = 0.5, SSS = 0, C* = $3.25
Deutsche Motorenwerke: Kab = 300, Kon = 600, P* = $15,000,000
Venture Sisters: TCL = QT&T = BC = $250,000; CM = $100,000; PME = $150,000; ER* = $205,500
Yamamoto—Revenue: Pir = 45, Buc = 100, R* = $770,000
Yamamoto—Cost: Pir = 10, Buc = 20, C* = $92,000
Yamamoto—Profit: Pir = 80, Buc = 53?, P* = $330,667
Café Café: (Tins) Esp-4 = 8640, Esp-8 = 4800, Cre-4 = 4080, Cre-8 = 2323?, Spu-4 = 6000, Spu-8 = 4560, P* = $269,531.83
Gecko: (Ads) BTV = 300, CTV = 333?, Print = 125, Billboards = 200, Airports = 4000, ARP* = 74,100
