What is a "corner point"? Explain why solutions to linear programming problems focus on cornerp points.
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Q: Explain why are the linear programming solutions are focused on corner points ?
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What is a "corner point"? Explain why solutions to linear programming problems focus on cornerp points.
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- Explain why are the linear programming solutions are focused on corner points ?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?Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graph
- City government has collected the following data on annual sales tax collections and new car registrations: Annual Sales Tax Collections (in millions) 1.0 1.4 1.9 2.0 1.8 2.1 2.3 2.5 New Car Registrations (in millions) 10 12 15 16 14 17 20 22 Determine the following: Plot these data and decide if a linear model is reasonable. Using the results of part a., find the estimated sales tax collections if new car registrations total 25,000,000.Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Consider the following linear programming problem: Maximize 6x+5y (OBJ) Subject to x+y≤6 (1) 2x+y≤8 (2) y≤5 (3) x,y≥0 What is the optimal solution to this problem? What is the optimal value of the objective function? Solve this model by using graphical analysis based on the Corner Point Solution Method. Answer questions below. 2.1. Clearly plot and label the constraints. Show your calculations for drawing constrain line. The solution without calculation will not be accepted. 2.2. Develop and shade the feasible region. Use graph paper. 2.3. Compute all the corner points or extreme points and their coordinates (i.e. the values of x and y). The solution without calculation will not be accepted. 2.4. Determine the optimal solution (i.e. the values of x and y) using corner points method. Why your solution is optimal? 2.5 Compute the value of the objective function at the optimal…
- What is meant by the term feasible solution space? What determines this region?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 11x + 5y + 10z subject to 8x + 12y + 19z ≥ 68 13x + 16y + 5z ≥ 136 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?How would you write the optimal solution for these?
- For the following linear programming problem, determine the optimal solution using the graphical solution method. Max −X + 2Y s.t. 6X − 2Y ≤ 3 −2X + 3Y ≤ 8 X + Y ≤ 3 X, Y ≥ 0 (X, Y) =The High-Price Oil Company owns a pipeline network that is used to convey oil from its source to several storage locations. A portion of the network is as follows: Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing sections of the pipeline network, the firm can supply any of the storage locations. a. If the firm wants to fully utilize the system capacity to supply storage location 7, how long will it take to satisfy a location 7 demand of 100,000 gallons? What is the maximal flow for this pipeline system? b. If a break occurs on line 2–3 and that line is closed down, what is the maximal flow for the system? How long will it take to transmit 100,000 gallons to location 7?State some key types of applications of the minimum spanning tree problem?