For each of the following programs:(1) Sketch the feasible region of the program and the direction of the objectivefunction.(2) Use you sketch to find an optimal solution to the program. State the optimalsolution give the objective value for this solution. If an optimal solution doesnot exist, state why.(3) Transform the program into standard equation form.(4) List all basic feasible solutions of your standard equation form program. Youshould give the values for both the original decision variables and the slackvariables in each of these basic feasible solutions.(a)maximise– 2x1 + x2Xị – x2 < 1,2.x1 – x2 > 1,subject to-2.x1 + 2x2 2 4,X1, x2 > 0(b)maximise xı+ 2x2subject to-x1 + 2x2 < 6,*1 + 3x212,X1, x2 > 0

Solution a: Given that maximize -2x1+12x2subject to x1-x2≤12x1-x2≥12x1+2x2≥4x1, x2≥0 The…

Answered: For each of the following programs: (1)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the per-day rate, 3 fewer cars are rented. They want to know what price they should rent at to maximize their revenue. Help them get started by setting up the revenue equation. You do not need to find the optimal price, just set up the revenue equation. Use x as your variable, but in your work be sure to define what a represents. Revenue =
A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 40 refrigerators already, while warehouse B has 15 on hand. It costs $10 to ship a refrigerator to warehouse A and $14 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost? Find the objective function and the constraints for the above problem.
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A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? I need to use the Five Step Method for mathematical modeling. Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency. Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math. Formulate the model. Restate…
A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? P(x)= -.5x2+15x+4700 P'(x)= -x+15 p"(x)= -1 < 0 SENSITIVITY ANALYSIS: (This is the part I am a bit uncertain about. The questions below.) Any help is much appreciated. 1. Preform a sensitivity analysis of the optimal time to sell versus the variable cost to raise a unicorn (harness still $100). 2. So if the actual variable cost was $4.00 per day instead of $5.00 (20% decrease), what would you estimate for the best time to sell based on your sensitivity results? 3. Finally, substitute $4.00 for the variable…

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