3. By using the data below, use an Assignment method to Operator Mach A 10 Mach B Mach C Mach D 2 8 9 11 9. 12 7 14 14 D 3 1 4 2 A. Formulate this linear programming model B. What is the optimal solution for the assignment method
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- c. Formulate Linear Optimization Models for the following: i. A company has been given a tender to supply maize to four drought zones. The cost of transporting each unit from the grains depot to the drought zone is given below: 1 | 2 | 3 4 Supply 1 21 16 25 | 13 17 18 14 23 13 3 32 27 18 41 19 Demand 10 12 15 43 6. 2.Jk.335. Propiem 14-8 Rent'R Cars is a multisite car rental company in the city. It is trying out a new "return the car to the location most convenient for you" policy to improve customer service. But this means that the company has to constantly move cars around the city to maintain required levels of vehicle availability. The supply and demand for economy cars, and the total cost of moving these vehicles between sites, are shown below. From To A B C Demand D $9 9 5 50 From/To $8 Candidate solution A B C Total shipped Cost A - B C Total costs 8 3 60 $6 8 3 25 $5 D 0 10 a. Find the solution that minimizes moving costs using Microsoft Excel. (Leave no cells blank - be certain to enter "0" wherever required.) Supply 50 40 75 30 165 165 E F G Supply $The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in the figure below; the openings between the rooms are numbered 1 through 13. Entrance Room 1 Room 2 1 4 8 12 Room 3 Room 4 7 Room 5 10 Room 6 2 5 13 Room 7 11 Room 8 A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two-way cameras.
- J 2 An electronics store wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)1. Cars are shipped from three distribution centre's to five dealers. The following table summarizes the mileage between the distribution center's and the dealers together with the monthly supply. Dealer 1 3 4 Supply 1 38 Center 2 3 4 19 3 4 4 16 4 4 9. 4 6. 23 Demand 25 29 21 | 21 a) Find the Initial basic feasible solution using any of the three methods. b) Check the Optimum solution using UV method.Problem 4-11 (Algorithmic) Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many units of each…
- (1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). B C 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route B 1 2 3 4 A 10 11 9 14 Step 1b: Column subtraction. Truck / Route 1 2 3 4 A 10-6=4 = = = = = B = с = C Step 2: Testing for optimal solution (show your lines covering the zero entries). What is the minimum number of lines required to cover all zeros? D 8 14 10 13 D = = D =REQUIRED: (a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains do not solve) 1 Question The Audiofile Company produces boomboxes. However, management has decided to subcontract out the production of the speakers needed for the boomboxes. Three vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers is shown below Vendor 1 2 3 In addition, each vendor would charge a shipping cost. Each shipment would go to one of the company's two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage data are shown below Vendor 1 2 3 Vendor 2 3 Warehouse 1 Price $22,500 $22,700 $22,300 Charge per shipment $300+0.40/m $200+050/mle $500+0.20/mile 1600 miles 500 miles 2,000…3. The Captain of a Cricket team has to allot 5 middle position to 5 batsmen. The average runs scored by each batsman at these positions are as follows Batting Positions III Batsmen II IV V P 40 40 35 25 50 27 50 42 30 16 25 R. 50 48 40 60 20 19 20 18 25 T 58 60 59 55 Find the assignment of batsmen to positions, which would give the maximum number of runs. If another batsman 'U' with the following average runs in batting positions as given below: Batting Positions: Average Runs: Is added to the team, should he be added to play in the team? If so, who should be replaced by him? II II IV V 45 52 38 50 49
- 1. Problem 13-14 (Algorithmic)The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:State of NatureDecision Alternative S1 S2 S3d1 200 150 75d2 250 150 50The probabilities for the states of nature are P(s1) = 0.5, P(s2) = 0.3 and P(s3) = 0.2.a. What is the optimal decision strategy if perfect information was available? S1 : d2 S2 : d1 or d2 S3 : d1 b. c. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. d. Using the expected value approach, what is the recommended decision without perfect information? d2 What is its expected value? If required, round your answer to one decimal place. e. What is the expected value of perfect information? If required, round your answer to one decimal place.1. In the mechanical workshop, 5 different jobs are to be assigned to 4 different machines. Assign each job on each one of the machines. Jobs / Machines 1 2 3 4 1 59 80 81 82 78 84 73 61 71 101 3 92 71 111 87 50 4 64 77 87 48 62 Solve the assignment problem by the Hungarian method. Also, Find the assignment of the job to a machine that will maximize the profit in OMR.A. Solve the following linear program by the solver method. P = 100x + 200y 3x + 3y 2 16 14x + 5y s 10 2x + 7y z 10 x, y 20 4. Maximize: Subject to: Solver Solution: B D E 1 Decision: 4 Constraints: Total Used Sign Available 5 1 6 2 7 3 8 Maximize P: 3.