The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Plant 1 2 3 1 1150 1450 950 Distribution Center. 2 3 1650 750 1750 950 1550 1150 4 1050 1350 1250 The freight cost for each shipment is $100 plus 50 cents per mile. Obtain an optimal solution, and determine the total cost. Total Cost = $ 27300
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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…Dennison Manufacturing makes large helical springs used in aircraft landing gear. The company has narrowed its potential choices for its new manufacturing facility to four cities. The following information is known about the manufacturing and shipping costs of locating in each of these four cities: Fixed Costsper Year Variable ManufacturingCosts per Unit Variable ShippingCosts per Unit Phoenix Buffalo Seattle Atlanta $300,000 $600,000 $1,500,000 $1,750,000 $70.00 $56.00 $36.00 $42.00 $5.00 $4.00 $2.00 $5.00 a. Use break-even point analysis to determine where Dennison should locate.b. Based solely on break-even quantity, if Dennison’s manufacturing forecast for the foreseeable future is 40,000 units annually, where should he locate?Mo. Samsung produces semiconductor chips in South Korea, China, and the United States. Products using these chips are sold around the world and therefore Samsung sells them on every continent. Below is the available supply and demand for all locations with the associated shipping costs. Supply (in millions) Demand (in millions) South Korea – 2.5 China – 3.5 United States – 2.0 North America – 2.1 South America – 1.4 Europe – 1.2 Africa – 1.1 Asia – 2.3 Australia – 0.8 Shipping Costs North America South America Europe Africa Asia Australia South Korea $12 $14 $9 $7 $3 $13 China N/A $15 $10 $8 $5 $16 United States $4 $6 $11 $17 N/A $18 Ongoing trade tensions between the United States and China have resulted in a ban on imports/exports. Additionally, the United States can only supply North America with 1.5 million and Australia requires at least 500,000 from South Korea. Using all this information, determine the optimal solution to the problem.
- A company has three plants at location A,B and C which produce the same product. It has to supply this to buyers located at P, Q and R. The weekly plant capacities for A, B and C are 250, 800 and 350 units respectively, while the buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit shipping cost (in Ksh) are given as Plant Buyer P Buyer Q Buyer R A 8 4 10 B 9 7 9 C 6 5 8 Determine the distribution for the company so as to minimize the cost of transportation using least cost method.Consider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abovConsider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.
- Find the optimal solution to this linear programming problem. Min 3X+3Y s.t. 12X+4Y>=60 10X+5Y>=60 4X+8Y>=36 X,Y>=0 (X,Y) = ( )May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000Suppose Jack like to solve the following formulation in Excel. And the problem is setup in Excel like this: See attached picture. A B C D E 1 X1 X2 2 decision variable objective 3 coefficient of objective function 2 3 4 Constraints LHS RHS 5 Constraints 1 2 1 3 6 Constraints 2 4 5 20 7 Constraints 3 2 8 16 8 Constraints 4 5 6 60 We want to put our objective function in cell D3. What should we type in D3? In cell D5 to D8, we will put the left hand side of our constraint. What should we type in D8? In OpenSolver, what should we assign to Variable Cell? What should you do to input the non-negativity constraint in OpenSolver?
- Compute the objective function value for the following problem: Min 30X + 150Y subject to : 2X>=0 ;2X + 10Y = 20; X+Y>=0 a. 0 b. 54 c. infeasible d. 300 e. unbounded(5) Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: _______________________________________________________________(c) Which of the following points yields the best solution? Underline the best solution: (7,5), (9,2), (6,6).Justify your answer (using the data from the above LP…Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 13x + 3y subject to 12x + 14y ≤ 21 15x + 20y ≤ 37 and x ≥ 0, y ≥ 0. What is the optimal value of x?