4) In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u₁ = -2, U2 = 3, U3 = 5, V₁ = 2, V2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
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- A retail store in Makkah, receives shipments of a particular product from Jeddah and Taif. Let X be units of product received from Jeddah and Y be units of product received from Taif.a. Write an expression for the total units of product received by the retail store in Makkah. b. Shipments from Jeddah cost $0.20 per unit, and shipments from Taif cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Makkah.c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Makkah. d. No more than 4000 units can be shipped from Jeddah and no more than 3000 units can be shipped from Taif in a month. Develop constraints to model this situation.e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Makkah retail store at minimum cost. i have here one point, why we are choose r…given the transportation problem, assume that the demands at the 4 destinations are 5, 5, 7, and 8 units, respectively, and the supplies at the 4 sources are 7, 3, 7 and 8 units, respectively.C₁₁=7ㅤ C₁₂=9ㅤ C₁₃ = 1ㅤ C₁₄ = 10 C₂₁= 22ㅤ C₂₂ = 25ㅤ C₂₃ = 16ㅤ C₂₄ = 26 С₃₁ = 28ㅤ C₃₂ = 32ㅤ C₃₃ = 24ㅤ Сз₄ = 32 C₄₁ = 12ㅤ C₄₂ = 14ㅤ C₄з = 6ㅤ C₄₄ = 16where m=4, n=4what is the optimal solution using vogel's approximation method, least-cost method, and northwest-corner rule?A retail store in Des Moines, Iowa, receives shipments of a particular product from KansasCity and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolisa. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost$0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model…
- HMO has 40 doctors to be apportioned among four clinics. The HMO decides to apportion the doctors based on the average weekly patient load for each clinic, given in the following table. Clinic A B C D Average Weekly 275 392 611 724 Patient Load Find the apportion of A and C using using Adam's Method. Use modified divisor 52. Doctors for clinic A Doctors for clinic B = %3D Doctors for clinic C= Doctors for clinic D =Let xj be the number of units allocated to supply-destination pair i (supply) and j (demand). If we use VAM as an initialization technique, which of the following supply- destination pairs will be allocated first? Destination 1 2 3 Supply 1 15 13 7 Source 2 11 17 5 3 9. 11 9. 3 Demand 3 ActivaA manufacturer sells a product in two regions. Weekly demand in each region is Normally distributed with mean 1,000 and standard deviation 300. Lead time is one week. Demand in the two regions has a correlation coefficient of -.35. They are considering two supply chain configurations: (1) A distribution center in each region, and, (2) a central distribution center that would serve demand from each region. Suppose they want to maintain a 95% service level (i.e. don’t stock out 95% of the time). How much more/less safety stock will there be in the configuration with a single distribution center?DO NOT COPY THE ANSWER FROM ANOTHER QUESTION ASKED PLEASE!!
- A company has three existing warehouses to which it will ship furniture from a new factory whose location must be decided. The factory will receive raw materials from its wood supplier and fabric supplier. The annual number of shipments, shipment costs and the location of the suppliers and warehouses are shown below Existing facilities Annual L to or from fact cost Coordinate location Wood supplier 120 10 (100, 400) Fabric supplier 200 10 (800,700) Ware h 1 61 10 (300, 600) Ware h 2 40 10 (200, 100) Ware h 3 70 10 (600, 200) Using the median load answer the following questions –Where the factory should be located to minimize annual transportation cost –What will be the minimum annual transportation costA company that has cement factories in Denizli, İzmir and Uşak will transport the cements to theconsumption region 1, 2 and 3. The cement production capacities of the factories are 200 tons forthe factory in Denizli, 300 tons for the factory in İzmir and 450 tons for the factory in Usak.Demand of the first consumption region is 250, demand of the second region is 100, demand of thethird region is 225 and demand of fourth region is 325 tons of cement. The transportation costbetween factories and consumption areas is as below table per ton:Factories 1. Region 2. Region 3. Region 4. RegionDenizli 15 18 12 13İzmir 10 10 11 9Usak 8 5 7 8According to these data;1) Make the initial distribution of the enterprise according to the Vogel’s Approximation Method(VAM) and calculate the total transportation cost. 2) Determine the distribution that minimizes the total transportation cost according to the (MODI)method.solve for y in part b
- Q: When we solve the given transportation problem according to the lowest cost method, which warehouse and/or warehouses are suitable for shipment from f3 (F: Factory M: Customer)A) no needb) M1, M2, M3c) M1 and M2d) M3 and M1E) M3Problem 1. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 20 salespeople given the information below. Shift Morning Midday Afternoon Evening The average number of customers 95 305 435 515 Determine the apportionment using Hamilton’s Method Jefferson’s Method Webster Method Huntington-Hill Method4. Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Set up the solution in Excel and solve with Solver. What are total costs?