Suppose you have a bounded feasible region with corner points (0,7),(3,4),(9,1), and (12,0). Find the minimum of the objective function C=3x+4y on this feasible region, as well as where it occurs.
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- A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment. Based on the Maximax criteria, the investor should choose Investment Motel Restaurant Theater Motel Restaurant O Theater O Any of the three Shortage $-8,000 2,000 6,000 Gasoline Availability Stable Supply $15,000 8,000 6,000 Surplus $20,000 6,000 5,000Dickie Hustler has $2 and is going to toss an unfair coin(probability .4 of heads) three times. Before each toss, hecan bet any amount of money (up to what he now has). Ifheads comes up, Dickie wins the number of dollars he bets;if tails comes up, he loses the number of dollars he bets.Use dynamic programming to determine a strategy thatmaximizes Dickie’s probability of having at least $5 afterthe third coin toss.We are going to see the movie Fatal Repulsion. Thereare three parking lots we may park in. One is one block eastof the theater (call this lot 1); one lot is directly behindthe theater (lot 0); and one lot is one block west of thetheater (lot 1). We are approaching the theater from the east.There is an 80% chance that lot 1 will have a vacantspace, a 60% chance that lot 0 will, and an 80% chance thatlot 1 will. Once we pass a lot, we can’t go back to it. Assumethat when we are at a given parking lot, we can determinewhether it has any vacant spaces, but we can’t see any ofthe other lots. Our dates for the evening will assess us apenalty equal to the distance (in blocks) that we park fromthe theater. If we find no space, they will assess a penaltyof 10 (and never go out with us again). What strategyminimizes our expected penalty? Answer the same questionif there is a 70% chance that lot 0 has a vacant space.
- Even though independent gasoline stations have been having a difficult time. Murad has been thinking about starting her own independent gasoline station. Murad's problem is to decide how large his station would be. The annual returns will depend on both the size of his station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Murad developed the following table: Size of the first station Small Medium Large Very large Probability Good market,$ 50 000 80 000 100 000 300 000 20% Fair market,$ 20 000 30 000 30 000 25 000 30% a) what is the maximax decision? b) what is the maximin decision c) what is the equally likely decision (Laplace) d) What is the Expected Monetary Value Criterion (EMV Criterion) Poor market, $ -10 000 -20 000 -40 000 -160 000 50%Long-Life Insurance has developed a linear model that it uses to determine the amount of term life Insurance a family of four should have, based on the current age of the head of the household. The equation is: y=150 -0.10x where y= Insurance needed ($000) x = Current age of head of household b. Use the equation to determine the amount of term life Insurance to recommend for a family of four of the head of the household is 40 years old. (Round your answer to 2 decimal places.) Amount of term life insurance thousandsPlease help to solve this
- Multiple Optimal Solution: Example (9): Find the optimal solution for the : Multiple Optimal following model by the graphical method Max Z = X,+X, X, +X, 23 .(1) X, +X, 56 S. to : X,21 ..(2) .(3) X, s2 (4) X, 20 X, 20Combined-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?For 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.
- Apply 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 problemDefine n/n problem with a suitable practical example. Multiple solution in case of certain n/2 problem? Explain.Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.