LP Problem and Solver for Winkler Furniture Production

Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table below contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. (a) Formulate as an LP problem.(b) Solve this problem using Excel solver.What would you suggest to Bob Winkler to solve his problem?(c) If the available painting hours are increased to 400 hours, will your answers in (b) change?PROBLEMS331c. minimize production losses.d. maximize the number of products to be produced.e. minimize the costs of nutrient blends.7. The diet problem isa. also called the feed mix problem in agriculture.b. a special case of the ingredient mix problem.c. a special case of the blending problem.d. all of the above.8. The selection of specific investments from among awide variety of alternatives is the type of LP problemknown asa. the product mix problem.b. the investment banker problem.c. the portfolio selection problem.d. the Wall Street problem.e. none of the above.Problems8-1(Production problem)Winkler Furniture manufac-tures two different types of china cabinets: a FrenchProvincial model and a Danish Modern model.Each cabinet produced must go through three de-partments: carpentry, painting, and finishing. Thetable below contains all relevant information con-cerning production times per cabinet produced andproduction capacities for each operation per day,along with net revenue per unit produced. The firmhas a contract with an Indiana distributor to producea minimum of 300 of each cabinet per week (or 60cabinets per day). Owner Bob Winkler would liketo determine a product mix to maximize his dailyrevenue.(a) Formulate as an LP problem.(b) Solve using an LP software program or spread-sheet.8-2(Investment decision problem)The Heinlein andKrampf Brokerage firm has just been instructed byone of its clients to invest $250,000 of her moneyobtained recently through the sale of land holdingsin Ohio. The client has a good deal of trust in the in-vestment house, but she also has her own ideas aboutthe distribution of the funds being invested. In par-ticular, she requests that the firm select whateverstocks and bonds they believe are well rated, butwithin the following guidelines:(a) Municipal bonds should constitute at least 20%of the investment.(b) At least 40% of the funds should be placed in acombination of electronic firms, aerospace firms,and drug manufacturers.(c) No more than 50% of the amount invested inmunicipal bonds should be placed in a high-risk,high-yield nursing home stock.Subject to these restraints, the client’s goal is to max-imize projected return on investments. The analystsat Heinlein and Krampf, aware of these guidelines,4. A typical transportation problem has 4 sources and 3 des-tinations. How many decision variables would there be inthe linear program for this?a. 3b. 4c. 7d. 125. A typical transportation problem has 4 sources and 3 des-tinations. How many constraints would there be in thelinear program for this?a. 3b. 4c. 7d. 126. When applying LP to diet problems, the objective func-tion is usually designed toa. maximize profits from blends of nutrients.b. maximize ingredient blends.Note: means the problem may be solved with QM for Windows; means the problem may be solved with Excel; and means the problem may be solved with QM for Windows and/or Excel.CARPENTRYPAINTINGFINISHING(HOURS/(HOURS/(HOURS/NET REVENUE/CABINET STYLECABINET)CABINET)CABINET)CABINET ($)French Provincial31.50.7528Danish Modern210.7525Department capacity (hours)360200125Data for Problem 8-1The Heinlein and KrampfBrokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines: (i) Municipal bonds should constitute at least 20% of the investment. (ii) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. (iii) No more than 50% of the amount invested in municipal bonds should be placed in high-­?risk, high-­?yield nursing home stock. Subject to these restraints, the client’s goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines, prepare a list of high-­?quality stocks and bonds and their corresponding rates of return:(a) Formulate this portfolio selection problem using LP. (b) Solve this problem using Excel solver.What would you suggest to the client?(c) If the projected rate of return of “Happy Days Nursing Homes” drops to 6.0% next year, would you suggest the client to invest it? Please explain based on your new findings using Excel solver.332CHAPTER 8 • LINEAR PROGRAMMING APPLICATIONSprepare a list of high-quality stocks and bonds andtheir corresponding rates of return:8-4(Animal feed mix problem)The Battery Park Stablefeeds and houses the horses used to pull tourist-filledcarriages through the streets of Charleston’s historicwaterfront area. The stable owner, an ex-racehorsetrainer, recognizes the need to set a nutritional diet forthe horses in his care. At the same time, he would liketo keep the overall daily cost of feed to a minimum.The feed mixes available for the horses’ diet arean oat product, a highly enriched grain, and a mineralproduct. Each of these mixes contains a certainamount of five ingredients needed daily to keep theaverage horse healthy. The table on this page showsthese minimum requirements, units of each ingredientper pound of feed mix, and costs for the three mixes.In addition, the stable owner is aware that anoverfed horse is a sluggish worker. Consequently, hedetermines that 6 pounds of feed per day are themost that any horse needs to function properly. For-mulate this problem and solve for the optimal dailymix of the three feeds.8-5The Kleenglass Corporation makes a dishwasherthat has excellent cleaning power. This dishwasheruses less water than most competitors, and it is ex-tremely quiet. Orders have been received from sev-eral retails stores for delivery at the end of each ofthe next 3 months, as shown below:PROJECTED RATE INVESTMENTOF RETURN (%)Los Angeles municipal bonds5.3Thompson Electronics, Inc.6.8United Aerospace Corp.4.9Palmer Drugs8.4Happy Days Nursing Homes11.8(a) Formulate this portfolio selection problem usingLP.(b) Solve this problem.8-3(Restaurant work scheduling problem).The fa-mous Y. S.