Consider the following network representation of a transportation problem:20JeffersonCityOmahaJefferson CityOmahaDemandOmahaJefferson CityIcon Key14Total Cost: $16103SuppliesDemandsThe supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below.DesMMoines02525KansasCity10515St.LouisDes Moines Kansas City St.Louis Supply10203002510Total Cost: $480.Find an alternative optimal solution for the above problem.If required, round your answer to nearest whole number and if your answer is zero enter "0".1510Des Moines Kansas City St.Louis

Find the Given details below: Transportation table From To Des Moines Kansas City St. Louis…

Answered: Consider the following network…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 46P

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Consider the following primal LP problem:Maximize X1 + 2X2 – 9X3 + 8X4 – 36X5Subject to 2X2 – X3 + X4 – 3X5 ≤ 40 X1 – X2 + 2X4 – 2X5 ≤ 10 X1 ≥ 0, X2 ≤ 0, X3 ≥ 0, X4 ≥ 0, X5 ≥ 0 (a) Write the dual of the LP above, using variables Y1, Y2, etc.(b) Sketch the feasible region of the dual LP in 2 dimensions, and use the graphical method to find the dual optimalsolution (Plot an isovalue line corresponding to the feasible solution, move the line in improving direction, findthe last one touching the feasible region, and any point(s) on the intersection of the last isovalue line andfeasible region are optimal solutions)(c) Using complementary slackness conditions, - write equations which must be satisfied by the optimal primal solution X* - which primal variables must be zero?(d) Using the information in (c), determine the optimal primal solution X* (e) Compare the optimal objective values of the primal and dual solutions
Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________
Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?
Mad Max wants to travel from New York to Dallas bythe shortest possible route. He may travel over the routesshown in Table 8. Unfortunately, the Wicked Witch canblock one road leading out of Atlanta and one road leadingout of Nashville. Mad Max will not know which roads havebeen blocked until he arrives at Atlanta or Nashville. ShouldMad Max start toward Atlanta or Nashville? Which routesshould the Wicked Witch block? Route (Miles)New York–Atlanta 800New York–Nashville 900Nashville–St. Louis 400Nashville–New Orleans 200Atlanta–St. Louis 300Atlanta–New Orleans 600St. Louis–Dallas 500New Orleans–Dallas 300
Jefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000 x √4= $1,600,000. Number of Warehouses Transportation Cost 4 8,000,000 5 6,500,000 6 5,000,000 7 4,400,000 a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost? b) Now suppose the…
A refinery manufactures two grades of jet fuel, Fl and F2, by blending four types of gasoline, A. B, C, and D. Fuel Fl uses gasolines A. B. C, and D in the ratio 1:1:2:4, and fucl F2 uses the ratio 2:2:1:3. The supply limits for A, B.C, and D are 1000, 1200, 900, and 1500 bbl/day, respectively. The costs per bbl for gasolines A, B, C, and D are $120, $90, $100, and $150, respectively. Fucls Fl and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2, and find the solution using Solver
A refinery manufactures two grades of jet fuel, Fl and F2, by blending four types of gasoline, A. B, C, and D. Fuel Fl uses gasolines A. B. C, and D in the ratio 1:1:2:4, and fucl F2 uses the ratio 2:2:1:3. The supply limits for A, B.C, and D are 1000, 1200, 900, and 1500 bbl/day, respectively. The costs per bbl for gasolines A, B, C, and D are $120, $90, $100, and $150, respectively. Fucls Fl and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2,
Fred Block Company has orders for 90 tons of concrete blocks at three suburban locations as follows: Northwood -- 25 tons, Westwood -- 45 tons, and Eastwood -- 20 tons. Fred has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is shown as follows Delivery Cost Per Ton Northwood Westwood Eastwood Plant1 20 30 40 Plant 2 30 40 45 a. Develop a network representation of this distribution problem. b. Develop a linear program model that can be used to determine the plan that will minimize total distribution costs. c. Solve the problem to describe the distribution plan and show total distribution cost.(Submit Excel files).

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