“It is essential to constrain all shipments in a transportation problem to have integer values to ensure that the optimal LP solution consists entirely of integer-valued shipments.” Is this statement true or false? Why?
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“It is essential to constrain all shipments in a transportation problem to have integer values to ensure that the optimal LP solution consists entirely of integer-valued shipments.” Is this statement true or false? Why?
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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.A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P05_54.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars.a. Determine how to minimize the cost of meeting demands in Houston and Tampa.b. Modify the answer to part a if no shipments through Atlanta are allowed.
- The optimal solution to the original Grand Prix problem indicates that with a unit shipping cost of $132, the route from plant 3 to region 2 is evidently too expensive—no autos are shipped along this route. Use SolverTable to see how much this unit shipping cost would have to be reduced before some autos would be shipped along this route.Explain what is meant by a linear programming that has feasible region with infinite number of solutions ?True or False 1. Given three corner points A, B, and C of a linear programming problem, if A is adjacent to B and B is adjacent to C, then A can be determined from C by interchanging exactly two basic and two nonbasic variables. 2. For a set of primary and dual solutions to be feasible, the objective function value of the primary (Z) can never exceed that of the dual (W) no matter which problem is to maximize and which is to minimize. 3. If the current iteration is degenerate, the next iteration will also be degenerate. 4. The optimal (dual) primary solution can be obtained from the dual (primary) optimal tableau.
- A company has four warehouses and six stores. The warehouses altogether have a surplus of 22 units of a given commodity, divided among them as follows: Warehouses 1 2 3 4 Surplus 5 6 2 9 The six stores altogether need 22 units of the commodity. Individual requirements at b stores 1,2,3,4,5 and 6 are 4,4,6,2,4 and 2 units respectively. Cost of shipping one unit of commodity from warehouse i to store j in $ dollars is given in the matrix below. Stores Warehouses 1 2 3 4 5 6 1 9 12 9 6 9 10 2 7 3 7 7 5 5 3 6 5 9 11 3 11 4 6 8 11 2 2 10 Required Formulate the mathematical model for the problem How should the products be shipped from the warehouses to the stores so that the transportation cost is minimum?A2 A healthy diet contains m different nutrients in quantities at least equal to b1, · · · , bm. This diet can be composed by choosing nonnegative quantities x1, · · · , xn of n different foods. One unit quantity of food j contains an amount aij of nutrient i, and has a cost of cj. Formulate this problem as an optimization problem in order to determine the cheapest diet that satisfies the nutritional requirements. What if we want to determine the most nutritious diet that does not exceed the cost given by the different foods? What is the relation between both formulations?Federated Oil has refineries in Los Angeles and Chicago. The Los Angeles refinery can refine up to two million barrels of oil per year, and the Chicago refinery up to three million. After the oil is refined, it is shippedto two distribution points, Houston and New York City. Federated Oil estimates that each distribution point can sell up to five million barrelsper year. Because of differences in shipping and refining costs, the profit earned (in dollars) per million barrels of oil shipped depends on where the oil was refined and on the point of distribution. This information is listed in the file P04_69.xlsx. The company is considering expanding the capacity of each refinery.Each million barrels of annual refining capacity that isadded will cost $120,000 for the Los Angeles refinery and $150,000 for the Chicago refinery. Determine how Federated Oil can maximize its profit (including expansion costs) over a 10-year period.
- 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 variableFairway Inc. makes custom golf clubs. They are manufactured in 3 plants in Denver, Phoenix, and Dallas. They are then shipped to distribution centers in Sacramento, Salt Lake, Chicago, Albuquerque, and New York. Since shipping costs are a major expense, management requires an analysis to determine the optimal shipping routes and quantities shipped along those routes. Each plant has a maximum production capacity and each distribution center has a demand that must be satisfied. You must determine how many clubs to send along each route, staying within plant capacity, meeting demand, for the lowest total shipping cost. Shipping Costs per route Plants Sacramento Salt Lake Chicago Albeq New York Capacity Denver $10 $8 $6 $5 $4 310 Phoenix $6 $5 $4 $3 $6 260 Dallas $3 $4 $5 $5 $9 280 Demand 180 80 200 160 220 Number to ship from plant to warehouse: Plants Sacramento Salt Lake Chicago Albeq New York Total Shipped Denver Phoenix…