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.
- 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 thisMultiple 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, 20
- 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?A country has two airfields with installations worth$2,000,000 and $10,000,000, respectively, of which it candefend only one against an attack by its enemy. Theenemy, on the other hand, can attack only one of these airfields and take it successfully only if it is left unde-fended. Considering the “payoff” to the country to be the total value of the installations it holds after the attack,find the optimum strategy of the country as well as thatof its enemy and the value of the “game.”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 problem
- Define n/n problem with a suitable practical example. Multiple solution in case of certain n/2 problem? Explain.A retail store in Des Moines, Iowa, receives shipments of a particular product from KansasCity and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolisa. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost$0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model…4 (b) An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for ( ) ,YΧ is given by the following table: Χ Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 i. Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance. ii. Find the probability that a randomly selected policy holder has a home deduction of at least K100. iii. Are the random variables Χ and Y independent? Explain your answer.