Consider the following Integer Linear Program: Minimise: 5x1 4x2 Subject to: X1 + X2 > 6 X1 + 4x2 > 12 3x1 + X2 > 9 X₁, X2 ≥ 0 and integer Construct the initial tableau for this problem including all decision, slack and artificial variables. You should assume the M-method will be used to solve this, so build the tableau with the objective function (i) +
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- Please do not give solution in image format thanku Let xi = 1 if Project i is selected, i = 1,2,3,4,5; and 0 otherwise: Which answer below indicates that if Project 2 is selected, then Project 4 must be selected? Group of answer choices None of the above x2 + x4 = 1 x2 + x4 ≤ 1 x4 ≤ x2 x2 ≤ x4Suppose Box I contains five red balls and two white ones while Box II contains one red and four white ones. A box is chosen at random by selecting a random number from 0 through 9. If a 1 or 2 is selected, Box I is chosen; otherwise Box II is chosen. If I took Box 1 and chose 2 balls without replacement, what is the proabability that exactly one would be red?Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.
- Scenario You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram below:Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.A political party is planning a half-hour television show. The show will have at least 3 minutos of direct requests for money from viowers Three of the party's politicians will be on the show-a senator, a congresswoman, and a governor The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor The total time taken by the senator and the governor must be at least twice the time taken y the congresswoman Based on a pre-show survey, it is believed that 33, 38, and 43 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers Find the maximum number of viewers The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, x, be the total number of minutes allottod to the congresswoman, and x,…
- 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.FRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.Please note that formulating linear program doesn't need coding but only modelling. It's operational Research problem. Garden House produces three custom flower seed mixes. Garden House is trying to decide how many pounds of each mix to produce for the upcoming planting season. All three mixes require two seed types, the all-star and the purple power. Garden house can obtain at most 25 lbs of all-star and 30 lbs of purple power seeds. Seed requirements, along with the revenue per pound of each, are given in Table 1, All star seeds cost $2/lb, and purple power seeds cost $3/lb. From past history, the company knows that it will be able to sell at most 60 lbs of mix A, but that they will sell as much of mix B and mix C as they produce. Formulate a linear program to help garden house maximize its profits.
- 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 problemFopic 4- Linear Programming: Appli eBook Problem 9-05 (Algorithmic) Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 ounces of hot sauce. Today, Kilgore has 21 pounds of beef, 16 cups of onions, 89 ounces of Kilgore's special sauce, and 61 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today.…minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2