Decision Making Problem

For capers 1-3 below, submit a non-technical foul consulting root word (approximately ? 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 let in a formulation of a linear model, as we did in course of action (decisions, objective, constraints), and standard printouts of the spreadsheet model with an optimal solution (see Instructions for Standard gradeouts below). fuss 1 Perfume (30 marks)Rylon Corporation manufactures brute(prenominal) and Chanelle perfumes. Raw material be $3 per pound. Processing a pound of raw material takes whizz hour of laboratory time, and yields 3 oz.s of uninterrupted 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 get along litigateing Regular Brute perfume to arise highlife Brute perfume, selling for $18/ounce. Each ounce of Regular Brute neat requires supererogatory 3 hours of laboratory time and yields one ounce of Luxury Brute at a address 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 pro check over? SKOLKOVO FT MBA trouble 2 Production & advertisement (35 marks) Your firm makes fluorescent paint pigments in four plants and ships them to four electrical distributors (abbreviated D1 through D4), as follows Plant Northeast south-east NorthwestSouthwest Unit Shipping Cost To D2 D3 Capacity Unit Cost Impurities D1 special K $ 12. 40 12 $ 1. 20 $ 1. 75 $ 2. 35 cxxv0 $ 11. 55 15 $ 1. 95 $ 1. 35 $ 1. 75 950 $ 10. 85 18 $ 2. 45 $ 1. 50 $ 2. 10 1200 $ 12. 05 12 $ 2. 75 $ 2. 25 $ 2. 00 D4 $ 2. 85 $ 2. 15 $ 1. 95 $ 1. 45 The distributors learn for the pigments is as follows D1 15. 0 scoop shovel Impurities 700 Base regard Advertising Sensitivity 0. 05 D2 15. 0 600 0. 1 D3 14. 0 550 0. 05 D4 15. 5 675 0. 125 For example, distributor D1 aloneow accept up to 700 units of pigment, plus 0. 05 units for every dollar bill 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, D1s demand depart be 700 + (0. 05)(100) = 705 units, D2s demand pass on be 600 + (0. 1)(100) = 610 units, D3s demand will be 555 units, and D4s 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 merge together, should come an average i mpurity level of at most 15. . You have at most $59,000 to spend on merchandise, shipping and advertising, and all the distributors buckle under you $28. 50 per unit. How can you maximize your pro foregathers? Note this problem combines blending, transportation, and elements of the pickles problem. 1) 2) hypothesise 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 designates for engines used in the manufacture of trucks.The turnout line is highly complex and measures 500 meters in length. Two symbols of engine heads are produced on the line the P-Head and the H-Head. The P-Head is used in heavy responsibleness 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 clothe up to manufacture the P-Head or the H-Head, but not both. C hangeovers from producing one type to the other are made on weekends and cost $500. The line has aptitude to produce the PHead at 100 units per week and the H-Head at 80 units per week.Kingston Manufacturing has merely shut down for the week and the line has been producing the PHead. The manager wants to plan production and changeovers for the contiguous eight weeks. Currently Buc profounde has an inventory of 125 P-Heads and 143 H-Heads. stocktaking carrying costs are charged at an annual rate of 19. 5% of the value of inventory. The production cost for the P-Head is $225 and for the H-Head is $310. The objective in developing a production enrolment is to minimize the sum of production cost, inventory carrying cost and changeover costs.Kingston Manufacturing has received the following requirements schedule from its customer (an engine assembler) for the succeeding(a) nine weeks. Week 1 2 3 4 5 6 7 8 9 Product Demand P-Head H-Head 55 38 55 38 44 30 0 0 45 48 45 48 36 58 35 57 35 58 Safety stock requirements are such that week-ending inventory must provide for at least 80% of beside weeks demand. You should prepare a production and changeover schedule report for the Kingston Manufacturing management to minimize total costs for the next eight weeks. (Hint To model the changeover costs, you may introduce a double star decision 1, if there is a changeover in week = 1, 8. allow a binary variable represent a decision whether to produce Pheads ( = 1) or H-heads ( = 0) in week , = 1, 8. Then you need the constraints which say that if you change the production in week from P-heads to H-heads or H-heads to P-heads, must be 1 ? ? 1 and ? 1 ? .) Instructions for Standard Printouts Throughout the course, I will ask for standard printouts of your Excel models.The standard printouts for a model live of two things. The first is a printout of the model as a fix of values, the way it usually appears on the screen. To get this printout, you perform the following step Go to Print/Page Setup. chitchat on the Sheet tab. If there is no X in the box next to Gridlines and Row and tower Headings, click there so that one appears. Click OK Click on the printer icon in the toolbar, or choose Print from the file menu to print the spreadsheet. If possible, you should try to make each spreadsheet printout fit on a single page.Under the Print/Settings select landscape orientation, and fit sheet on one page before you print. The second printout should be as a set of formulas. It should show the formulas in your spreadsheet for optimization models (which will be most of our spreadsheets), it should also clearly indicate the physical object cell, the ever-changing cells, and all constraints. Also indicate whether you are minimizing or maximizing the manoeuver cell. To get this printout, follow these steps Type control-tilde (hold down ctrl and type the key marked ) Adjust the chromatography column widths so that you can see all the formulas.Print out the spreadsheet, using the same procedure as above. To indicate the target cell, minimization or maximization, changing cells, and constraints, you may make handwritten notations on this second printout. Alternately, you may make notations using text and graphics on the spreadsheet itself. Excel will let you draw arrows right on your spreadsheet. Points will be deducted if you fail to follow these guidelines. Common errors are forgetting the row and column headings, or not clearly indicating the changing cells, target cell, or constraints. To go back to the values view, type control-tilde