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.
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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.
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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.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.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.
- “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?In a typical network model representation of the transportation problem, the nodes indicate a. roads b. rail lines c. geographic locations d. rivers For all routes with positive flows in an optimized transportation problem, the reduced cost will be: a. zero b. how much less shipping costs would have to be for shipments to occur along that route c. how much more shipping costs would have to be for shipments to occur along that route d. how much the capacity is along that shipping route The decision variables in transportation problems are: a. profits b. costs c. flows d. capacities Which of the following statements is a type of constraint that is often required in blending problems? a. Integer constraint b. Quality constraint c. Binary constraint d. None of these options When a workforce…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 $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.
- The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 6x1 + 3x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 (a) Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ------ to -------- (b) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ----- to -------- (c) Compute the dual value for the first constraint, second constraint & third constraintShortest path problem A company sells seven types of boxes, ranging in size from 17 to 33 cubic feet. The demand and size of each box is given in the table below. The variable cost ($) of producing each box is equal to the box’s size. A fixed setup cost of $1000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size. Formulate a shortest path model to minimize the cost of meeting the demand for boxes. Box 1 2 3 4 5 6 7 Size 33 30 26 24 19 18 17 Demand 400 300 500 700 200 400 200 The unit cost (in dollars) of producing each box is equal to the box’s size, for example, $24 per box of type 4 (with size 24). A fixed setup cost of $1000 is incurred to produce a particular size of boxes. For example, if you produce at least one box of type 5, there is a fixed setup cost of $1000, no matter how many boxes of type 5 to produce; the setup cost for type 5 is zero, if no boxes of type 5 are produced. Only formulate…The standard form of the following linear programming model is given. Find the values of variables at the point of intersection of constraint 1 and the vertical axis (y). (Round your answers to 3 decimal places.) Maximize P = 30x + 15y + 0s1 + 0s2 subject to 6x + 12y + s1 = 19 13x + 12y + s2 = 35 and x, y, s1, s2≥ 0.
- Use linear programming and the graphing approach to find the optimal solution to the following problem. Transportation: An anthropology class is planning to rent buses and vans for a trip to the Field Museum in Chicago. A bus can transport 25 students, requires 2 adult supervisors and costs $550 to rent. A van can transport 10 students, requires 1adult supervisor and costs $200 to rent. The organizers must plan seating to accommodate at least 150 students. Only 14 parents are available,so the travel plans must allow for at most 16 adult supervisors. How many vehicles of each type should be rented to minimize the rental cost? What is the minimum rental cost for the trip?Solve these problems using graphical linear programming and answer the questions that follow. Usesimultaneous equations to determine the optimal values of the decision variables.a. Maximize Z = 4x1 + 3x2Subject toMaterial 6x1 + 4x2 ≤ 48 lbLabor 4x1 + 8x2 ≤ 80 hrx1, x2 ≥ 0 b. Maximize Z = 2x1 + 10x2Subject toDurability 10x1 + 4x2 ≥ 40 wkStrength 1x1 + 6x2 ≥ 24 psi Time 1x1 + 2x2 ≤ 14 hrx1, x2 ≥ 0 c. Maximize Z = 6A + 3B (revenue)Subject toMaterial 20A+ 6B ≤ 600 lbMachinery 25A+ 20B ≤ 1,000 hr Labor 20A+ 30B ≤ 1,200 hrA, B ≥ 0 (1) What are the optimal values of the decision variables and Z?Solve 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.