Introduction to Management Science, 13thGlobal (Bernard W. Taylor III) (z-lib.org).pdf - Adobe Acrobat Pro DC X File Edit View Window Help Home Tools Document 130 (131 of 864) 75% x Sign In LL Bookmarks X minimize Z = 8.2x] + 7.0x2 + 6.5x3 + 9.0x4 subject to Search Tools... 6x1 + 2x2 + 5x3 + 7x4 2 820 - 2 0.3 * +x2 + x3 + x4 Create PDF Cover *2 + 23 = 0.2 x1 + X4 X3 2 X1 + X4 Title Page *1, *2, *3, X4 20 Edit PDF Copyright Page transform the model into standard form and solve by using the computer. Export PDF 55. Tracy Mccoy has committed to the local PTA to make some items for a bake sale on Saturday. She Brief Contents has decided to make some combination of chocolate cakes, loaves of white bread, custard pies, and sugar cookies. Thursday evening she goes to the store and purchases 20 pounds of flour, 10 Contents pounds of sugar, and 3 dozen eggs, which are the three main ingredients in all the baked goods she Comment is thinking about making. The following table shows how much of each of the main ingredients Preface is required for each baked good: Organize Pages 1 Management Science Ingredient Flour (cups) Sugar (cups) Eggs Baking Time (min.) Enhance Scans 2 Linear Programming: Cake 2.5 45 Model Formulation and Bread 9 0.25 0 35 Graphical Solution Pie 1.3 50 Protect Cookies 25 16 3 Linear Programming: Computer Solution and Le Fill & Sign There are 18.5 cups in a 5-pound bag of flour and 12 cups in a 5-pound bag of sugar. Tracy plans Sensitivity Analysis to get up and start baking on Friday morning after her kids leave for school and finish before they return after soccer practice (8 hours). She knows that the PTA will sell a chocolate cake for 4 Linear Programming: $12, a loaf of bread for $8, a custard pie for $10, and a batch of cookies for $6. Tracy wants to Prepare Form Modeling Examples decide how many of each type of baked good she should make for the PTA to make the most money possible. 5 Integer Programming x& Send for Signature Formulate a linear programming model for this problem. 6 Transportation, 56. Solve the linear programming model formulated in Problem 55 for Tracy Mccoy. ->.. Send & Track Transshipment, and a. Are any of the ingredients left over? b. If Tracy could get more of any ingredient, which should it be? Why? Assignment Problems c. If Tracy could get 6 more eggs, 20 more cups of flour, or 30 more minutes of oven time, which 7 Network Flow Models should she choose? Why? d. The solution values for this problem should logically be integers. If the solution values are not integers, discuss how Tracy should decide how many of each item to bake. How do total sales 8 Project Management for this integer solution compare with those in the original, noninteger solution? 9 Multicriteria Decision 57. A manufacturer produces stationeries-binder clips, pencils, erasers, and sharpeners-and packs them in boxes. A box of binder clips will have 12 pieces of binding clips; a pencil box, Activate Wistoreand share files in the Making 12 pencils; sharpener box, 20 pieces of sharpeners; eraser box, 10 pieces of erasers. The fol- lowing table shows the resource requirements. Go to Settings to actRacyment Cloud 10 Nonlinear Learn More Programming Type here to search O W 24'C Sunny ~ 9 4 () ENG 6:03 PM 994 2022-06-03 EIntroduction to Management Science, 13thGlobal (Bernard W. Taylor III) (z-lib.org).pdf - Adobe Acrobat Pro DC X File Edit View Window Help Home Tools Document 131 (132 of 864) 75% x Sign In LL Bookmarks X Search Tools... CASE PROBLEM 131 Binder clips Pencils Erasers Sharpeners Available Create PDF Cover Labor minutes required 12 32 20000 Packaging in units 10 6 7000 Title Page Space in cm2 11 10 10 14000 Edit PDF Profit per box in AED 16 Copyright Page The manufacturer wants to determine how many boxes of each product they need to pack to Export PDF Brief Contents maximize profits. Formulate a linear programming model to this problem. Contents Comment 58. Solve the linear programming model formulation in Problem 57 using computer. a. Are there any extra (slack) resources available? Preface b. If the manufacturer could obtain additional resources, which one would be of most value to Organize Pages them? How much would they be willing to pay for this resource? Why? 1 Management Science c. If the manufacturer could reduce the total space availability, how much space can they reduce? Enhance Scans 2 Linear Programming: 59. Guanming wants to paint houses and commercial buildings during his summer vacation. He Model Formulation and has two types of customers-residential and commercial. The profit from a residential property is HKD500 and from a commercial property, HKD750. A residential property takes 3 hours to Graphical Solution paint while a commercial, 4 hours. He likes to work for 48 hours a week. He has a budget of Protect 3 Linear Programming: HKD600 per week toward brushes and other consumables. A residential property needs HKD80 toward such tools and consumables, while a commercial property, HKD40. He decides based Computer Solution and on his experience that he cannot get more than 6 residential jobs and 8 commercial jobs. He Le Fill & Sign Sensitivity Analysis wants to know how many residential and commercial jobs he should complete to maximize his profits. 4 Linear Programming: a. Formulate a linear programming model to this problem. Prepare Form b. Solve this model graphically. Modeling Examples 60. Solve the linear programming model in Problem 59 using the computer. 5 Integer Programming a. Which resources constrain how many jobs Guanming can contract for? x& Send for Signature b. Guanming wants for increase either his working hours per week by 10 hours or increase the 6 Transportation, budget by HKD100. Which would you recommend? . The solution for this problem should logically be an integer. If not, use the computer and find ->.. Send & Track Transshipment, and the optimum integer values. How much does his profit deviate from his non-integer optimum? Assignment Problems 7 Network Flow Models Case Problem 8 Project Management MOSSAIC TILES, LTD. derivative for their tiles. Their manufacturing operation con- 9 Multicriteria Decision sists of a few relatively simple but precarious steps, include Activate Wistoreand share files in the Making ing molding the tiles, baking, and glazing. Gilbert Moss and Angela Pasaic spent several summers Gilbert and Angela plan to produce two basic types of Go to Settings to actRacyment Cloud 10 Nonlinear during their college years working at archaeological sites tile for use in home bathrooms, kitchens, sunrooms, and in the Southwest. While at those digs, they learned how to laundry rooms. The two types of tile are a larger, single- Learn More Programming make ceramic tiles from local artisans. After college they colored tile and a smaller, patterned tile. In the manufac Type here to search O 24 C Sunny ~ 9 4 () ENG 6:04 PM 994 E 2022-06-03