Given four decision variables A, B, C, and D, which of the following could be a linear programming problem constraint? 1A + 2B - 1C/D >=23 1A + 2A*B + 3A*B/C + 4A*B*C*D >=100 1A + 2B + 3C + 4D >=100 1A + 2B/C + 3D <=45 1A + 2B*C + 3D <=100
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Given four decision variables A, B, C, and D, which of the following could be a linear programming problem constraint?
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1A + 2B - 1C/D >=23 |
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1A + 2A*B + 3A*B/C + 4A*B*C*D >=100 |
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1A + 2B + 3C + 4D >=100 |
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1A + 2B/C + 3D <=45 |
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1A + 2B*C + 3D <=100 |
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- a.) Formulate a LP model of this problemFor the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________
- Don't solve. Please give- Decision Variable Constraint Objective functionIn problems involving maximization and minimization, what is the objective function? States intended outcome in equation form Incorporates constraint of maximum budget Lists set of potential restrictions on the solution Cites constraints to ensure objectivityApply Linear Programming to the Folling Question: Dan Reid, chief engineer at New Hampshire Chemical, Inc., has to decide whether to build a new state-of-art processing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, New Hampshire Chemical could lose $150,000. At this time, Reid estimates a 60% chance that the new process will fail. The other option is to build a pilot plant and then decide whether to build a complete facility. The pilot plant would cost $10,000 to build. Reid estimates a fifty-fifty chance that the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plant does not work, there is only a 20% chance that the complete project (if it is constructed) will work. Reid faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision? Help Reid by analyzing this problem
- A young computer engineer has $12,000 to invest and three different investment options (funds) to choose from. Type 1 guaranteed investment funds offer an expected rate of return of 7%, Type 2 mixed funds (part is guaranteed capital) have an expected rate of return of 8%, while an investment on the Stock Exchange involves an expected rate of return of 12%, but without guaranteed investment capital. Computer engineer has decided not to invest more than $2,000 on the Stock Exchange in order to minimize the risk. Moreover for tax reasons, she needs to invest at least three times more in guaranteed investment funds than in mixed funds. Assume that at the end of the year the returns are those expected; she is trying to determine the optimum investment amounts. (a) Express this problem as a linear programming model with two decision variables.(b) Solve the problem with the graphical solution procedure and define the optimum solution.Please show how to solve b3 II | Here are the changes to the original problem and the revised conditions for this decision-making problem: With a favorable market, John Thompson thinks a large facility would result in a net profit of $195,000 to his firm. If the market is unfavorable, the construction of a large facility would result in $185,000 net loss. A small plant would result in a net profit of $110,000 in a favorable market, but a net loss of $25,000 would occur if the market was unfavorable. Doing nothing would result in $0 profit in either market conditions. a) Create a decision table, b) What is your recommendation if you would apply the Maximax criterion (Optimistic)? Follow the guidance from your textbook and create a table. c) What is your recommendation if you would apply the Maximin Criterion (Pessimistic)? Follow the guidance from your textbook and create a table. d) What is your recommendation if you would apply the Criterion of Realism (Hurwicz Criterion) with a coefficient of realism a =…
- Combined-cycle power plants use two combustion turbines to produce electricity. Heat from the first turbine’s exhaust is captured to heat waterand produce steam sent to a second steam turbine that generates additional electricity. A 968-megawatt combined-cycle gas fired plant can be purchased for $450 million, has no salvage value, and produces a net cash flow(revenues less expenses) of $50 million per year over its expected 30-year life. Solve, a. If the hurdle rate (MARR) is 12% per year, how profitable an investment is this power plant? b. What is the simple payback period for the plant? Is this investment acceptable?b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°C3. (Note: This is a variation of problem 6 of chapter 16 in your textbook.) Kenya and Dionne live on adjacent plots of land. Each has two potential uses for their land, the present values of each of which depend on the use adopted by the other, as summarized in the table. All the values in the table are known to both parties. Dionne Rental housing Bee keeping Kenya Apple growing A: $200 B: $700 A: $400 B: $650 Pig farming A: $450 B: $400 A: $450 B: $500 a. What is the efficient outcome? b. If there are negotiation costs of $150, what activities will the two pursue on their land? c. If there are no negotiation costs and the two negotiate, what activities will the two pursue on their land? How might a benevolent planner help reduce the costs of negotiating to encourage the optimal combination of land uses?