A transportation problem mvolves the following costs, supply and demand. From/ To A B Supply 1. 12 10 9. 600 2. 4. 15 400 3. 7. 300 4. 11 8. 800 Demand 900 500 900 Find the initial solution using northwest corner method, the minimum cell cost method and VAM. Find the optimal solution using stepping stone and MODI. b. a.
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in Table below. The company’s goal is to minimize the cost of meeting customers’ demands. From To Customer 1 Customer 2 Customer 3 Supply Plant 1 55 65 80 35 Plant 2 10 15 25 50 Demand 10 10 10 Formulate a linear programming (LP) model for this problem. Use solver to find the optimal transportation rule As a management science student, the MD of the company seeks your expert advice on ways in which to determine the optimal transportation rule. Advise the MD, providing detailed explanation using your answer obtain in (b). Write your answer in a form of a report to the MD.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: ______________________________________________________________
- Please use excel for this problem A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table: Machine Country Contemporary Total Machine Time Available Per Week Router 3.5 4.0 1,000 Sander 4.5 6.5 2,000 Polisher 3.0 2.0 1,500 Country tables sell for $395 and contemporary tables sell for $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.An individual wishes to invest PhP 50,000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%. Market research recommends an allocation of at least 25% of the actual total investment in A and at most 50% of the actual total investment in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments? questions: -Find the feasible region -Find the corner points -Find the optimal valueSolve the following problems using Excel Solver or R Studio. A company produces cars in Atlanta, Boston, Chicago, and Los Angeles. The cars are then shipped to warehouses in Memphis,Milwaukee, New York City, Denver, and San Francisco. The number of cars available at each plant is given in Table 1. Eachwarehouse needs to have available the number of cars given in Table 2. The distance (in miles) between the cities is given inTable 3. Assuming that the cost (in dollars) of shipping a car equals the distance between two cities, determine an optimalshipping schedule.
- Transportation Problem: A semi-products manufacturer has 3 production facilities (X, Y, Z) and distributes its products to 3 various customers (K, L, M) from these production facilities. The daily production capacity of each production facility and the daily distribution costs are given in the below table. Daily demands of customers are 42, 27, and 33, respectively. Namely, in a day, customer K requires 42 units of products, customer L requires 27 units of products, and customer M requires 33 units of products. (a) Formulate a balanced transportation problem that could be used to determine how to minimize the total cost of meeting the demand of customers. The formulation should be in open form and decision variables should be defined as integer amounts. (b) Use LINGO/OPL/EXCEL to solve your model. Write down the results of the decision variables and the objective function. Explain the value of the decision variables. What do they mean? (c) Use the Northwest Corner method to find a…Two poultry farms supply companies with chicken feeds. The unit costs of shipping from the farms to the companies are given on the table below. The farm's goal is to minimize the cost of meeting customer's demands. For questions a and b; (a) Generate a mathematical model for finding the least cost way of shipping chicken feeds from the farms to the companies. (b) if the demand of company number 2 increased by 3 units. By how much would the costs increase? Show solution. (c). Solve the total cost using the solver add-in in excel.We illustrated how a machine replacement problem can be modeled as a shortest path problem. This is probably not the approach most people would think of when they first see a machine replacement problem. In fact, most people would probably never think in terms of a network. How would you model the problem? Does your approach result in an LP model?
- 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 SolverA 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,At the end of a cycle of schedules, a trucking firm has a surplus of one vehicle each in cities A, B, C, D, E, and F and a deficit of one vehicle each in cities 1, 2, 3, 4, 5, and 6. The distances between cities with a surplus and the cities with a deficit are shown below. Find an assignment of surplus vehicles to deficit cities that will result in a minimum total distance. What is the total distance? -Solve the following transportation models using Excel Solver. -Find the optimal solution for the transportation problem having the cost and requirement tablebelow.