a. Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. b. Solve the problem in part (a).
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Linear programming is a method of operation optimization with specific restrictions. The main objective of linear programming is to increase or reduce a numerical value. A common method for assessing the best use of resources is linear programming. An example of a linear programming problem is one that aids in identifying the feasible area and optimizing the solution to obtain the highest or lowest function value.
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- Consider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (0.0,0.0) is: a. infeasible. b. is one of the extreme points. c. the optimal solution. d. unboundedConsider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (0.0,6.0) is: a. the optimal solution. b. is one of the extreme points. c. infeasible. d. unbounded.A linear programming problem is given as follows:min ? = −4?1 + ?2Subject to 8?1 + 2?2 ≥ 164?1 + 2?2 ≤ 12?1 ≤ 6?2 ≤ 4?1, ?2 ≥ 0 I) Find the A, B, C, D, E, F, and G points on the plot below II) Identify the feasible solution area graphically on the following plot (by shading thearea) III) Which points are the extreme points IV) What is the solution of the optimization problem? (x1=?,x2=?,z=?) Show your work V) Which change will make the problem have multiple optimal solutions? If there is more than one answer, choose all.a) Increase of the coefficient of ?1 on the objective function to 4b) Increase of the coefficient of ?1 on the objective function to 2c) Decrease of the coefficient of ?1 on the objective function to -8d) Increase of the coefficient of ?2 on the objective function to -8e) None VI) If new constraints, ?1≤4 and ?2≤6, are added to the given problem, what effect will be? (choose all the effects)a) The feasible solution area will be smaller.b) The feasible solution area will…
- (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…Given the region of feasible solutions with corner points of (0,3), (4,2), (6,3), and (6,6), find the corner point that would minimize the objective function z = x +10y and state the minimum. Question 3 options: 66 3 24 36the Problem. The DISTRIBUTION UNLIMITED CO. will be producing the same new product at two different factories, and then the product must be shipped to two warehouses, where either factory can supply either warehouse. The distribution network available for shipping this product is shown in Fig. 3.13, where F1 and F2 are the two factories, W1 and W2 are the two warehouses, and DC is a distribution center. The amounts to be shipped from F1 and F2 are shown to their left, and the amounts to be received at W1 and W2 are shown to their right. Each arrow represents a feasible shipping lane. Thus, F1 can ship directly to W1 and has three possible routes (F1 → DC → W2, F1 → F2 → DC → W2, and F1 → W1 → W2) for shipping to W2. Factory F2 has just one route to W2 (F2 → DC → W2) and one to W1 (F2 → DC → W2 → W1). The cost per unit shipped through each shipping lane is shown next to the arrow. Also shown next to F1 → F2 and DC → W2 are the maximum amounts that can be shipped through these lanes. The…
- 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…Here is a problem to challenge your intuition. In theoriginal Grand Prix example, reduce the capacity ofplant 2 to 300. Then the total capacity is equal to thetotal demand. Reoptimize the model. You should findthat the optimal solution uses all capacity and exactlymeets all demands with a total cost of $176,050. Nowincrease the capacity of plant 1 and the demand atregion 2 by 1 automobile each, and optimize again.What happens to the optimal total cost? How can youexplain this “more for less” paradox?Consider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 Which of the following is the optimal solution? a. (2.0,2.0) b. (3.0, 1.5) c. (4.0,6.0) d. (6.0,0.0)
- 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 ≥ 5000A 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 transportation table below. REQUIREDa. Define the decision variablesb. Write a linear programming model for this problem.c. Use the Northwest-Corner Method, the Least-Cost Method and the VAM to getthe starting feasible solution.d. Find the optimal solution using the transportation algorithm discussed in class by considering the least optimal of the objective function computed in (c).e. Formulate a network model to illustrate the optimal solution