6. The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Distribution Center 1 800 miles 1100 miles 600 miles Distribution Center 2 1300 miles 1400 miles 1200 miles Distribution Center 3 400 miles 600 miles 800 miles Distribution Center 4 Plant 1 Plant 2 Plant 3 The freight cost for each shipment is $100 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? (a) Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Draw the network representation of this problem. (c) Use Excel Solver to obtain an optimal solution. 700 miles 1000 miles 900 miles
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- A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. D1 D2 D3 D4 Capacity S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Find initial basic feasible solution for given problem by usingcolumn minima methodif the object is to minimize the total transportation cost.A company has three manufacturing plants (in Atlanta,Tulsa, and Springfi eld) that produce a product that is then shipped to one of four distribution centers. Th e three plants can produce13, 18, and 12 truckloads of product each week, respectively. Eachdistribution center needs 10 truckloads of product each week. Th eshipping costs per truckload between the plants and distributioncenters are given in the table. Th e company needs to determinehow much to ship from each plant to each distribution center andwould like to minimize total shipping costs (a) Formulate an LP to minimize the total shipping costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolutionA health Centre will be built to serve 7 communities. The geographical location of the communities and their population is shown in the table below. Communities A, X =2.5 (km), Y=4.5(km), Population( 000's)=2 Communities B, X =2.5 (km), Y=2.5(km), Population( 000's)=5 Communities C, X =5.5 (km), Y=4.5(km), Population( 000's)=10 Communities D, X =5 (km), Y=2(km), Population( 000's)=7 Communities E, X =8 (km), Y=5(km), Population( 000's)=10 Communities F, X =7 (km), Y=2(km), Population( 000's)=20 Communities G, X =9 (km), Y=2.5(km), Population( 000's)=14 There is a possibility of building the Centre in two communities, community C and F. Based on the Demand-Distance criterion what is your recommendation for the site of the Centre. The distances to be measured based on Rectilinear method. Based on…
- (5) 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: _______________________________________________________________(c) Which of the following points yields the best solution? Underline the best solution: (7,5), (9,2), (6,6).Justify your answer (using the data from the above LP…Solve the following problem after finding its dual. Min z = x1 - 3x2 + 3x3 s.t. 3x1 - x2 + 2 x3 ≤ 7 2x1 + 4x2 ≥ -12 -4x1 + 3x2 + 8x3 ≤ 10 x1, x2, x3 ≥ 0The logistic company headquartered in New York wants to expand its business in Chicago, Texas, and Las Vegas. They will place 3 branch heads (A, B a, nd C) from several branch offices owned by the company to set-up offices and run operations in these 3 locations. Below are the costs for allocating the 3 branch heads to each location: Chicago Texas Las Vegas A $8,000,000 $11,000,000 $12,000,000 B $5,000,000 $15,000,000 $13,000,000 C $5,000,000 $10,000,000 $23,000,000 a. Create a table using the assignment method.b. Based on the results of your calculations, what advice can you give to the leader of the company for the most optimum companylocation placement of each of the above branch heads? Explain why?c. What is the total optimum cost that must be incurred by the company to allocate all company branch offices?
- The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…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).
- The Child-fair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distribution centers is given below. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost, where the freight cost for each shipment is $100 plus 50 cents/mile? Formulate this case as a transportation problem (a) algebraically, and (b) on a spreadsheet, then (c) use Solver to obtain the optimal solutionsA pizza company plans to open new stores in different locations. They consider 6 possible new locations. There are 9 potential areas each location can serve which are listed in the following table. Location Areas Served L1 3,4,8 L2 1,2,5 L3 1,4,7 L4 2,6,9 L5 3,5,9 L6 6,8,7 Each area must be served by at least one location. What is the minimum number of locations?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: ______________________________________________________________