Operations Research Formulate an LP model for the following problems.1. A furniture company makes two products: book shelves selling for P5,000 andcabinets selling for P8,000. The direct cost per unit is P3,000 and P4,000,respectively. The company has no difficulty in selling all the products it canmanufacture. The assembly department has 60 hours available per week and thefinishing department can handle up to 48 hours of work per week. Manufacturingone book shelf requires 4 hours in assembly and 2 hours in finishing. Eachcabinet requires 2 hours in assembly and 4 hours in finishing. How can themanagement allocate the limited man-hour of the two departments in a waywhich will secure the largest possible net return?

Let x and y be the number of bookshelves and cabinets respectively. Objective function: Max…

Answered: Formulate an LP model for the following…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 35P

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It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
Formulate an LP model for the following problems.1. A furniture company makes two products: book shelves selling for ₱5,000 and cabinetsselling for ₱8,000. The direct cost per unit is ₱3,000 and ₱4,000, respectively. Thecompany has no difficulty in selling all the products it can manufacture. The assemblydepartment has 60 hours available per week and the finishing department can handleup to 48 hours of work per week. Manufacturing one book shelf requires 4 hours inassembly and 2 hours in finishing. Each cabinet requires 2 hours in assembly and 4hours in finishing. How can the management allocate the limited man-hour of the twodepartments in a way which will secure the largest possible net return?
The following table represents sales data for milk (in hundred liters) sold by a grocery.Do the computations to fill out the table and answer the following questions:1. Using MAD as the criterion, which of the following models would you use for thegiven time series data? Why?A. Naïve approach;B. 5-month SMA model;C. WMA model with weights 0.1, 0.3, and 0.6; orD. ES model with α = 0.5 and a forecast of 3,500 liters in the first month.NOTE: In answering Item 1, mention the whole description of the model; i.e., not just“SMA model”, but “SMA model with n = ...”; not just “WMA model”, but “WMA modelwith weights ...”; not just “ES model”, but “ES model with α = ...”.2. Interpret the MAD of the most accurate among the forecasting models above.3. Based on your decision in Item 1, what should be the forecast for Month 11?
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8-1 (Production problem) 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 on this page 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. Cabinet Style Carpentry (Hours/Cabinet) Painting (Hours/Cabinet) Finishing (Hours/Cabinet) Net Revenue/Cabinet ($) French Provincial 3 1.5 0.75 28 Danish Modern 2 1 0.75 25 Department Capacity (Hours) 360 200 125 a) Formulate as an LP problem. b) Solve using an LP software program or…
8-1 (Production problem) 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 on this page 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. Perform the four steps (i.e., define variables, determine objective function, identify constraints, list the non-negativity statement) and write equations. Use the table in the picture
Define the decision variables ,Formulate the objective function, Formulate the constraints Sears Investment has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Bank regulations require diversification to the extent that a t least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as California and Texas, it is decided that no more than 40% of the investment be placed in bonds. How much should Sears Investment invest in each security so as to maximize its return on investment?
Management Science: XY Company manufactures and sells LCD monitor at P5000 each. The production officer reported the following: Sale price: P5000 per monitor direct materials cost: P1000 per unit direct labor cost: P550 per unit other overhead cost P950 per unit Fixed costs related to the production are also reported: salary of management: P200,000 rent for the factory: P150,000, other salaries: P140,000 depreciation of equipment: P12,000Compute the total variable cost
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The Scottville "Mill" produces five different fabrics. Each fabric can be woven on one or more of the mill's 38 looms. The sales department has forecast demand for the next month. The demand data are shown in Table 1.0 below along with data on the selling price per yard, variable cost per yard, and purchase price per yard. The mill operates 24 hours a day and is scheduled for 30 days during the coming month. The Mill has two types of looms: dobbie and regular. The dobbie looms are more versatile and can be used for all five fabrics. The regular looms can produce only three of the fabrics. The Mill has a total of 38 looms: 8 are dobbie and 30 are regular. The rate of production for each fabric on each type of loom is given in Table 1.1. The time to change over from producing one fabric to another is negligible and does not have to be considered. The Scottsville Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at…
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