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Rift Valley University
Masters of Business Administration program
Individual Assignment for the course Quantitative Analysis for Managerial Decision making
(20 Marks)
Attempt all the questions!
 Explain the milestones in the development of OR/MS/DS/SS.
 Discuss the similarities and differences between minimization and maximization problems using thegraphical solution approaches of LP
 Develop your own set of constraint equations and inequalities and use them to illustrate graphically eachof the following conditions:
(a) An unbounded problem
(b) An infeasible problem
(c) A problem containing redundant constraints
 Under what condition is it possible for an LP problem to have more than one optimal solution?
 Under what condition that we decided as the LP problem have unbounded solution, infeasible solution and Degenerate in Graphic, simplex and transportation model? How degeneracy problem is solved in simplex and transportation model?
 Discuss the role of sensitivity analysis in LP. Under what circumstances is it needed, and under what conditions do you think it is not necessary?
 A linear program has the objective of maximizing profit = 12X + 8Y.The maximum profit is $8,000.Using a computer we find the upper bound for profit on X is 20 and the lower bound is 9. Discuss the changes to the optimal solution (the values of the variables and the profit) that would occur if the profit on X were increased to $15. How would the optimal solution change if the profit on X were increased to $25?
 Develop your own original LP problem with two constraints and two real variables.
(a) Explain the meaning of the numbers on the righthand side of each of your constraints.
(b) Solve your problem graphically to find the optimal solution.
(c) Illustrate graphically the effect of increasing the contribution rate of your first variable by50% over the value you first assigned it. Does this change the optimal solution?
 Is the transportation model an example of decisionmaking under certainty or decision making under uncertainty? Why?
 What is a balanced transportation problem? Describe the approach you would use to solve an unbalanced problem.
 Explain what happens when the solution to a transportation problem does not have occupied squares (where number of rows in the table and number of columns in the table)
 Give an example of a good decision that you made that resulted in a bad outcome. Also give an example of a bad decision that you made that had a good out come. Why was each decision good or bad?
 Discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty.
 What techniques are used to solve decisionmaking problems under uncertainty? Which technique results in an optimistic decision? Which technique results in a pessimistic decision?
 Define opportunity loss. What decisionmaking criteria are used with an opportunity loss table?
 What information should be placed on a decision tree?
 Describe how you would determine the best decision using the EMV criterion with a decision tree
Attempt all the following word problems and show all the necessary steps you follow to answer the required questions.
18. The Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labor hours in the painting and varnishing department. Each table takes 4 hours of carpentry and 2 hours in the painting and varnishing shop. Each chair requires 3 hours in carpentry and 1 hour in painting and varnishing. During the current production period, 240 hours of carpentry time are available and 100 hours in painting and varnishing time are available. Each table sold yields a profit of $70; each chair produced is sold for a $50 profit. Flair Furniture’s problem is to determine the best possible combination of tables and chairs to manufacture in order to reach the maximum profit.
Required:
A. Develop a Linear Programing Model.
B. Change the LPP into standard form.
C. Solve the LPP by using;
 Graphical method
 Simplex algorithm method
 Identify the unused resources.
 Test for post optimality.
19. The Holiday Meal Turkey Ranch is considering buying two different brands of turkey feed and blending them to provide a good, lowcost diet for its turkeys. Each feed contains, in varying proportions, some or all of the three nutritional ingredients essential for fattening turkeys. Each pound of brand 1 purchased, for example, contains 5 ounces of ingredient A, 4 ounces of ingredient B, and 0.5 ounce of ingredient C. Each pound of brand 2 contains 10 ounces of ingredient A, 3 ounces of ingredient B, but no ingredient C. The brand 1 feed costs the ranch 2 cents a pound, while the brand 2 feed costs 3 cents a pound. The minimum requirements of Ingredient A, B & C are 90, 48 &1.5 ounces. The owner of the ranch would like to use LP to determine the lowestcost diet that meets the minimum monthly intake requirement for each nutritional ingredient.
Required:
 Formulate a LPP.
 Change the LPP in to its standard form.
 Solve the LPP by using;
a. Graphical method
b. Simplex algorithm method
c. Check for its post optimality (Sensitivity analysis)
20. A Medical Supply Company produces catheters in packs at three productions facilities. The company ships the packs from the production facilities to four warehouses. The table shows the costs per pack to ship to the four warehouses.
To
From 
Seattle

New York  Phoenix  Miami  Supply

Juarez  19  3  7  21  100 
Seoul  15  21  18  6  300 
Telaviv  11  14  15  22  200 
Demand  150  100  200  150  600 
Required:
 Form a general linear programing form (standard form).
 Find the optimum solution by using; 1. NWM, 2. Leastcost method, 3. VAM and check its optimality by using;
a. Steppingstone method
b. MODI for evaluation purpose.
21. A marketing manager in XYZ Company wants to assign 4 salespersons to 4 regions. The table below summarizes the expected monthly sales revenue (in 1000’s of Br.) that can be generated by each sales person in each region.
Regions  
Sales Person  West  South  East  North 
Alemu  50  40  35  42 
Bedada  35  30  29  27 
Chaltu  28  40  25  38 
Ahmed  26  35  30  34 
Required:
a. Form the general linear programing/ the standard form.
b. Fi nd the assignment schedule that maximizes expected sales revenue.
c. What is the expected total revenue?
22. Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced toconsider purchasing some more equipment forBro wn Oil because of competition. His alternativesare shown in the following table:
EQUIPMENT  FAVORABLE MARKET($)  UNFAVORABLE MARKET($) 
Sub 100  300,000  –200,000 
Oiler J  250,000  –100,000 
Texan  75,000  –18,000 
For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. But Ken has always been a very optimistic decision maker.
(a) What type of decision is Ken facing?
(b) What decision criterion should he use?
(c) What alternative is best?
23. Although Ken Brown (discussed in above illustration)is the principal owner of Brown Oil, his brotherBob is credited with making the company afinancial success. Bob is vice president of finance.Bob attributes his success to his pessimistic attitude about business and the oil industry. Given theinformation from Problem number 22, it is likely thatBob will arrive at a different decision. What decision criterion should Bob use, and what alternative will he select?
24. The Lubricant is an expensive oil newsletter towhich many oil giants subscribe, including KenBrown (see Problem 22 for details). In the lastissue, the letter described how the demand for oilproducts would be extremely high. Apparently, theAmerican consumer will continue to use oil products even if the price of these products doubles.Indeed, one of the articles in the Lubricantstates that the chances of a favorable market for oilproducts was 70%, while the chance of an unfavorable market was only 30%. Ken would like touse these probabilities in determining the bestdecision.
(a) What decision model should be used?
(b) What is the optimal decision?
(c) Ken believes that the $300,000 figure for the Sub100 with a favorable market is too high. Howmuch lower would this figure have to be for Kento change his decision made in part (b)?
25. Cal Bender and Becky Addison have known each other since high school. Two years ago they entered the same university and today they are taking undergraduate courses in the business school. Both hope to graduate with degrees in finance. In an attempt to make extra money and to use some of the knowledge gained from their business courses, Cal and Becky have decided to look into the possibility of starting a small company that would provide word processing services to students who needed term papers or other reports prepared in a professional manner. Using a systems approach, Cal and Becky have identified three strategies. Strategy 1 is to invest in a fairly expensive microcomputer system with a highquality laser printer. In a favorable market, they should be able to obtain a net profit of $10,000 over the next two years. If the market is unfavorable, they can lose $8,000. Strategy 2 is to purchase a less expensive system. With a favorable market, they could get a return during the next two years of $8,000. With an unfavorable market, they would incur a loss of $4,000. Their final strategy, strategy 3, is to do nothing. Cal is basically a risk taker, whereas Becky tries to avoid risk.
a. What type of decision procedure should Cal use? What would Cal’s decision be?
b. What type of decision maker is Becky? What decision would Becky make?
c. If Cal and Becky were indifferent to risk, what type of decision approach should they use? What would you recommend if this were the case?
Special cases
26. Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium and highpriced golf bags. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations:
a. Cutting and dyeing the material
b. Sewing
c. Finishing (inserting umbrella holder, club separators, etc.)
d. Inspection and packaging
The director of manufacturing analyzed each of the operations and concluded that if the company produces a mediumpriced standard model, each bag will require ⁷⁄₁₀ hour in the cutting and dyeing department, ¹⁄₂ hour in the sewing department, 1 hour in the finishing department, and ¹⁄₁₀ hour in the inspection and packaging department. The more expensive deluxe model will require 1 hour for cutting and dyeing, ⁵⁄₆ hour for sewing, ²⁄₃ hour for finishing, and ¹⁄₄ hour for inspection and packaging.Par’s production is constrained by a limited number of hours available in each department. After studying departmental workload projections, the director of manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for finishing, and 135 hours for inspection and packaging will be available for the production of golf bags during the next three months
The accounting department analyzed the production data, assigned all relevant variable costs, and arrived at prices for both bags that will result in a profit contribution of $6.3 for every standard bag and $9 for every deluxe bag produced.
 Formulate LP models
 Compute the optimal solution of the LPP by using Graphical method
 Suppose that management specified that at least 500 of the standard bags and at least 360 of the deluxe bags must be manufactured. Compute the optimal solution of the LPP by using Graphical method.
 Assume at least 600 hours are available for sewing section. Formulate LP model and solve the optimal solution of the LPP by using Graphical method.