QUESTION ONEA) Use graphical methodto solve following LP problem.Maximize z = 2x, + xsubiect to the constraintsX,+ 2x, < 10x, + 2x, S1B)Jse the penalty (Big - M) method to solve the following LP problem.Minimize Z = x, + 2x, + 3x, - xsubject to the constraintsX1+ 2x, + 3x3 = 152x1 + 2x, +5x = 20X1 + 2x, + x3 +x = 10

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Practical Management Science

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Chapter2: Introduction To Spreadsheet Modeling

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

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33 White & Becker Tools (W&B) requires 2,000 elec- tric motors next month for its product line of weed trimmers. Each motor is composed of three com- ponents: a coil, a shaft, and housing. W&B has the capability to produce these components or purchase them from an outside vendor. The costs of produc- ing them and purchasing them are shown in the following table. COMPONENT Coil Shaft Housing DEPART- MENT PRODUCTION COST PER UNIT Fabrication 0.5 Molding 0.4 Inspection 0.2 $2.60 $1.80 $1.40 The components that are produced by W&B must pass through three departments: fabrication, molding, and inspection. The number of hours each component requires in each department and the total number of hours available next month in each department are shown in the following table: 0.2 0.7 0.3 PURCHASE COST PER UNIT COIL SHAFT HOUSING AVAILABILITY (HR.) (HR.) (HR.) (HR.) $3.12 $2.16 $1.68 0.6 0.3 0.4 3,000 3,000 1,800 In order to determine the number of components that will be produced and the number…
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2. Four products are processed sequentially on three machines in an aircraft maintenance workshop. The following Table 1 gives the operational data of the problem. Machine 1 2 3 Unit selling price ($) Table 1: Operational data for the problem Manufacturing time (hr) per unit Cost per hr Product Product Product Product $ 1 3 4 10 2 4 2 5 1 2 4 2 1 55 45 37 75 2323 70 Capacity (hr) 500 380 450 (a) Formulate the problem as a Linear Programming (LP) problem (b) Determine the optimal product-mix in the production schedule and the optimal profit
A renowned chocolatier, Francesco Schroeder, makes three kinds of chocolate confectionery: artisanal truffles, handcrafted chocolate nuggets, and premium gourmet chocolate bars. He uses the highest quality of cacao butter, dairy cream, and honey as the main Ingredients. Francesco makes his chocolates each morning, and they are usually sold out by the early afternoon. For a pound of artisanal truffles, Francesco uses 1 cup of cacao butter, 1 cup of honey, and 1/2 cup of cream. The handcrafted nuggets are milk chocolate and take 1/2 cup of cacao, 2/3 cup of honey, and 2/3 cup of cream for each pound. Each pound of the chocolate bars uses 1 cup of cacao butter, 1/2 cup of honey, and 1/2 cup of cream. One pound of truffles, nuggets, and chocolate bars can be purchased for $35, $25, and $20, respectively. A local store places a daily order of 10 pounds of chocolate nuggets, which means that Francesco needs to make at least 10 pounds of the chocolate nuggets each day. Before sunrise each…
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Aa6. please solve with formulas not excell
14. Toyco produces a line of Bonnie dolls and accessories at its plants in New York and Baltimore that must be shipped to distribution centers in Chicago and Los Angeles. The company uses Air Freight, Ic., to make its shipments. Suppose that it can ship directly or through Pittsburgh and Denver. The daily production rates at the plants are respectively 5,000 and 7,000 units daily, and the demands at the dis- tribution centers are respectively 3,500 and 8,500 units daily. The costs of shipping 1,000 units are given in the following table. Find the optimal shipping routes and the associated cost. то Pittsburgh Denver Chicago Los Angeles $182 77 F New York Baltimore $375 290 275 $285 245 125 $460 575 380 R Pittsburgh M Denver 90 110
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JN Company manufactures two products that use material 1, material 2, and material 3. Consider the following table: Resources needed Material 1 Material 2 Material 3 Price per Unit in Pesos Requirement per Unit Product 1 2 2 0 150 Product 2 3 1 4 200 a. Write the linear programming model for this problem. b. Present the optimal solution and interpret the result. Maximum Availability (units) 1200 1000 800 c. Determine the status of each resource. d. Determine the dual prices for the materials 1, 2 and 3. Explain each value. e. Determine the feasibility ranges for the dual prices obtained in (d). f. If the available number of material 1 is increased to 1300 units, find the new optimum solution. g. Find the range of optimality for (i.) product 1 and (ii.) product 2 for which the optimal. solution remains valid.
A. Solve the following linear program by the solver method. P = 100x + 200y 3x + 3y 2 16 14x + 5y s 10 2x + 7y z 10 x, y 20 4. Maximize: Subject to: Solver Solution: B D E 1 Decision: 4 Constraints: Total Used Sign Available 5 1 6 2 7 3 8 Maximize P: 3.
1. Consider four bases of operation B, and three targets T, The tons of bombs per aircraft from any base that can be delivered to any target are given in the following table: Target (T;) T2 T3 Base (B;) B2 6 6 B3 10 8 4 B4 8 4 The daily sortie capability of each of the four bases is 150 sorties per day. The daily requirement of sorties spread over each individual target is 200. Find the allocation of sorties from each base to each target which maximizes the total tonnage over all three targets. Explain each step in the process. B,

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A) Use graphical methodto solve following LP problem. Maximize z = 2x, + x; subiect to the constraints *, + 2x, S 10 *, + x 56 *, + 2x, S1

A) Use graphical methodto solve following LP problem. Maximize z = 2x, + x; subiect to the constraints , + 2x, S 10 , + x 56 *, + 2x, S1