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- A company has three plants at location A,B and C which produce the same product. It has to supply this to buyers located at P, Q and R. The weekly plant capacities for A, B and C are 250, 800 and 350 units respectively, while the buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit shipping cost (in Ksh) are given as Plant Buyer P Buyer Q Buyer R A 8 4 10 B 9 7 9 C 6 5 8 Determine the distribution for the company so as to minimize the cost of transportation using least cost method.9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its Des Moines factory and to cut back the production capacities at its other two factories. It also recognizes a shifting market for its desks and revises the requirements at its three warehouses. The table on this page provides the requirement at each of the warehouses, the capacity at each of the factories, and the shipping cost per unit to ship from each factory to each warehouse. Find the least-cost way to meet the requirements given the capacity at each factory.Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…
- the Problem. The DISTRIBUTION UNLIMITED CO. will be producing the same new product at two different factories, and then the product must be shipped to two warehouses, where either factory can supply either warehouse. The distribution network available for shipping this product is shown in Fig. 3.13, where F1 and F2 are the two factories, W1 and W2 are the two warehouses, and DC is a distribution center. The amounts to be shipped from F1 and F2 are shown to their left, and the amounts to be received at W1 and W2 are shown to their right. Each arrow represents a feasible shipping lane. Thus, F1 can ship directly to W1 and has three possible routes (F1 → DC → W2, F1 → F2 → DC → W2, and F1 → W1 → W2) for shipping to W2. Factory F2 has just one route to W2 (F2 → DC → W2) and one to W1 (F2 → DC → W2 → W1). The cost per unit shipped through each shipping lane is shown next to the arrow. Also shown next to F1 → F2 and DC → W2 are the maximum amounts that can be shipped through these lanes. The…A chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, andchocolates.A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a…Four proposals are being considered with investment and NPW shown below. C can only beconsidered if B is implemented. B and D and E are mutually exclusive. The budget is $80.A B C D EInvestment $10 $20 $30 $40 $50NPW $34 $28 $20 $16 $32a) Formulate this as a 0-1 integer program (objective function and constraints).b) Use trial and error to find all feasible solutions, and indicate which is optimal.c) Set up this problem in Excel, and use Solver to find the same optimal solution
- Mo. Samsung produces semiconductor chips in South Korea, China, and the United States. Products using these chips are sold around the world and therefore Samsung sells them on every continent. Below is the available supply and demand for all locations with the associated shipping costs. Supply (in millions) Demand (in millions) South Korea – 2.5 China – 3.5 United States – 2.0 North America – 2.1 South America – 1.4 Europe – 1.2 Africa – 1.1 Asia – 2.3 Australia – 0.8 Shipping Costs North America South America Europe Africa Asia Australia South Korea $12 $14 $9 $7 $3 $13 China N/A $15 $10 $8 $5 $16 United States $4 $6 $11 $17 N/A $18 Ongoing trade tensions between the United States and China have resulted in a ban on imports/exports. Additionally, the United States can only supply North America with 1.5 million and Australia requires at least 500,000 from South Korea. Using all this information, determine the optimal solution to the problem.May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 500046. Ford is going to produce a new vehicle, the Pioneer,and wants to determine the amount of annual capacityit should build. Ford’s goal is to maximize the profitfrom this vehicle over the next five years. Each vehicle will sell for $19,000 and incur a variable production cost of $16,000. Building one unit of annual capacity will cost $2000. Each unit of capacity will alsocost $1000 per year to maintain, even if the capacityis unused. Demand for the Pioneer is unknown butmarketing estimates the distribution of annual demandto be as shown in the file P09_46.xlsx. Assume thatthe number of units sold during a year is the minimumof capacity and annual demand. Which capacity levelshould Ford choose? Do you think EMV is the appropriate criterion?
- Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 4 4 5 4 5 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) The minimum number of workers is 7 workers. (Enter your response as a whole number.) Specify the workforce schedule for each employee by indicating the day offs (other days are considered to be…Consider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements areDay M T W Th F S SuRequirements 6 3 5 3 7 2 3Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have two consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S–Su pair in case of a tie.