Q4. Solve the following LP problem by using The Simplex Algorithm. (Keep loyal to theSimplex Tableau Format you have learnt during the lectures.)Max z = 2x1 - x2 + x3s.t.3x1 + x2 + x3 ≤60x1 - x2 + 2x3 ≤ 10x1 + x2-x3 ≤20x1, x2, x3 ≥ 0

Here, I would convert this LP problem into a canonical form, in each constraint I would add the…

Answered: Q4. Solve the following LP problem by…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 3
1 ton of material 1 ton of material 2, and 11/13 3 10 The Kashif Corporation blends three raw materials to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of ton of material 1 and 3 ton of material 3. A ton of solvent base is a mixture of // Kashif's production is constrained by a limited availability of the three raw materials. For the current production period, Kashif has the following quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following P, priority level goals. Goal 1: Produce at least 30 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. Assume there are no other goals. (a) Is it possible for management to achieve both P₁ level goals given the constraints on the amounts of each material available? If not, which constraint is the limiting factor? O Yes. It is possible to satisfy both P₁ level goals. O No. There is an insufficient…
Hardgrave Machine Company produces computer components at its factories in Cincinnati, Kansas City, and Pittsburgh. These factories have not been able to keep up with demand for orders at Hardgrave’s four warehouses in Detroit, Houston, New York, and Los Angeles. As a result, the firm has decided to build a new factory to expand its productive capacity. The two sites being considered are Seattle, Washington, and Birmingham, Alabama. Both cities are attractive in terms of labour supply, municipal services, and ease of factory financing. Table 1 presents the production costs and monthly supplies at each of the three existing factories, monthly demands at each of the four warehouses, and estimated production costs at the two proposed factories. Transportation costs from each factory to each warehouse are summarized in Table 2. In addition to this information, Hardgrave estimates that the monthly fixed cost of operating the proposed facility in Seattle would be $400,000. The…
This home work question is based on a "Product Mix" problem For formulations, you don't need to explain it. Just state the formulation and constraints
Hh4. What is the total cost of meeting customer requirements each day?
b) The figure below presents an unbounded feasible region of a five constrained LP problem. 10- |(0, 6) 6. (1, 4) 4 (3, 2) 2+ (9, 0) 8 10 i. Write down in terms of x and y the inequalities that represent these constraints. ii. If the objective function is Z = 0.12x + 0.15y, determine the optimal solution to this problem (show the movement of the isocost line). ii. Identify the binding and non-binding constraints.
1. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.
Discuss the process of Refining Alphas, and why this process is a good alternative to constrained optimization.
3. Hoosier Gasoline Company, or HoosCo as they are known, produces two blends of gasoline, regular and premium, by mixing three different types of oil, indi- cated by Types 1, 2, and 3. Each type of oil comes in barrels and has its own costs and octane readings, which are given below. Type I Type 2 Type 3 Cost/Barrel $45 $35 $20 Octane Rating Regular gasoline Premium gasoline Regular gasoline 93 91 87 To produce each blend of gasoline, we must combine these oils so as to meet the following requirements. Premium gasoline Maximum Available 10,000 15,000 20,000 At least 25% Type 1 At least 35% Type 2 At most 30% Type 3 At least 30% Type 1 At least 45% Type 2 At most 20% Type 3 There are also sales prices, average octane rating requirements for the gasolines, and minimum requirements in production of each blend. Average Octane Rating Sales Price 89 91 $65 $75 Minimum Demand 15,000 barrels 12,500 barrels How much of each type of gasoline should be produced to satisfy all require- ments and…
Variable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…

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