Consider the transportation problem having the cost and requirement table a. Write the linear programming model for this problem. b. Use the Excel Solver to find the optimal solution. c. Draw a network showing the quantities obtained and the optimal value of z. Interpret the result. below. 9 2 4 Demand 30 Source N 3 Destination 2 3 7 6 4 3 3 35 800⁰ 20 4 4 10 5 25 Supply 50 30 30
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- Modify the warehouse location model as suggested inModeling Issue 2. Specifically, assume that the samefour customers have the same annual shipments, butnow, there are only two possible warehouse locations,each with distances to the various customers. (Thesedistances, along with other inputs, are in the fileP07_27.xlsx.) The company can build either or bothof these warehouses. The cost to build a warehouseis $50,000. (You can assume that this cost has beenannualized. That is, the company incurs a buildingcost that is equivalent to $50,000 per year.) If onlyone warehouse is built, it will ship to all customers. However, if both warehouses are built, then the com-pany must decide which warehouse will ship to each customer. There is a traveling cost of $1 per mile.a. Develop an appropriate model to minimize totalannual cost, and then use Solver to optimize it.Is this model an NLP or an IP model (or both)?b. Use SolverTable with a single input, the traveling costper mile, to see how large…Explain in detail Consider a balanced transportation problem with the cost of transportation Cij given by: C11=10,C12=0,C13=20,C14=11C11=10,C12=0,C13=20,C14=11, C21=12,C22=7,C23=9,C24=20C21=12,C22=7,C23=9,C24=20 , C31=0,C32=14,C33=16,C34=18C31=0,C32=14,C33=16,C34=18, with the current basic feasible solution (BFS): x12=15,x22=0,x23=15,x24=10,x31=5,x34=0x12=15,x22=0,x23=15,x24=10,x31=5,x34=0. Then Select one: a)current solution is not optimal and x24x24 is a leaving variable b)None of these c)the current BFS is optimal d)current solution is not optimal and x23x23 is a leaving variableConsider the following linear program: Max 3A + 3B S.t. 2A + 4B < 12 6A + 4B < 24 A, B > 0 Find the Optimal Solution using the graphical solution procedure If the objective function is changed to 2A + 6B, what will the optimal solution be? How many extreme points are there? What are the values of A and B at each extreme point?
- Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graphTwo 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.
- The following table shows the cost to ship goods from Factory 1,2,3 to Warehouse A,B,C: We will designate "F" as the variable for Factory. The constraint that represents the quantity supplied by Factory 1 should be written as: A)F1A+F1B+F1C=500 B)4F1A+6F1B+8F1C<=500 C)F1A+F1B+F1C<=500 D)F1A+F1B+F1C>=500 E)F1A+F2A+F3<=200Here is a problem to challenge your intuition. In the original Grand Prix example, reduce the capacity of plant 2 to 300. Then the total capacity is equal to the total demand. Run Solver on this model. You should find that the optimal solution uses all capacity and exactly meets all demands with a total cost of $176,050. Now increase the capacity of plant 1 and the demand at region 2 by 1 automobile each, and run Solver again. What happens to the optimal total cost? How can you explain this “more for less” paradox?consider the following network representation of a transportation problem:(The image provided) The supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below. Des Moines Kansas City St.Louis Supply Jefferson City 20 0 10 30 Omaha 10 10 0 20 Demand 30 10 10 Total Cost: $530. 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” Des Moines Kansas City St.Louis Jefferson City Omaha Total Cost: $ is?
- Max 30x1 x2 s.t. 2x1 x2 ≤ 4 2x1 2x2 ≤ 6 x1, x2 ≥ 0 (a) Solve graphically and state the optimal solution. (b) Keeping all the other data as is, what per unit profitability should the product, whose current optimal value is zero, have in order that this product enter the optimal solution at a positive level? (c) How many optimal corner solutions exist after making the change described in part (b)? What are they? (d) In the original problem, how much can the right-hand side (RHS) of the second constraint be increased (or decreased) before the optimal solution is changed? (e) Answer part (d) for the RHS of the first constraint. (f) How do you explain the difference between parts (d) and (e)? (g) What will be the impact of adding the constraint 4x1 x2 = 4 to the original model? (h) What is the impact (on the optimal solution) of adding the constraint 3x1 3x2 ≤ 15 to the original model? (i) Fill in the blanks: The difference between parts (g) and (h) is that the original optimal solution…Oranges are grown, picked, and then processed and pack-aged at distribution centers in Tampa, Miami, and Fresno. These centers supply oranges to markets in New York,Philadelphia, Chicago, and Boston. The following tableshows the shipping costs per truckload ($100s), supply,and demand: Because of an agreement between distributors, ship-ments are prohibited from Miami to Chicago. Solve this problem. to Newfrom York Philadelphia Chicago Boston SupplyTampa $ 9 $14 $12 $17 300Miami 11 10 6 10 200Fresno 12 8 15 7 250Demand 160 210 130 180Problem 7-14 (pg 278) Using the following equations, graph the constraints and solve using the corner point approach ONLY. Let: X1 = number of air conditioners to be produced X2 = number of fans to be produced Maximize profit = 25X1 + 15X2 subject to 3X1 + 2X2 <= 240 (wiring) 2X1 + 1X2 <= 140 (drilling) X1, X2 >= 0