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- 3 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 =…Q3:A/ Find the solution to the following linear programming problem by dual simplex method Min Z= 2X₁+4X₂ Subjected to: 2X₁-4X₂+2X3 ≥8 4X₁+2X₂-2X3 ≥ 12 X1, X2, X3 20Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin 2
- Four qualified postgraduate students are to be allocated to four professors. The preference given by student (scale 1-10) is shown as table below. Student A В C D Professor James Jordan Janet 7 8 6. Jessy 5 8. 7 (a) Formulate a linear programming model for the problem. [NOTE: Please use x, where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student to represent your decision variables.] (b) From the output below, what is the optimal allocation plan and what is the total preference scales obtained from the allocation plan? Model Variable Original Value Final Value Value x11 1 1 Value x12 1 Value x13 1 Value x14 Value x21 Value x22 Value x23 1 1 1 1 1 Value x24 1 Value x31 Value x32 Value x33 1 1 1 1 Value x34 1 Value x41 1 Value x42 1 Value x43 1 Value x44 1 1 699 4451. Problem 13-14 (Algorithmic)The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:State of NatureDecision Alternative S1 S2 S3d1 200 150 75d2 250 150 50The probabilities for the states of nature are P(s1) = 0.5, P(s2) = 0.3 and P(s3) = 0.2.a. What is the optimal decision strategy if perfect information was available? S1 : d2 S2 : d1 or d2 S3 : d1 b. c. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. d. Using the expected value approach, what is the recommended decision without perfect information? d2 What is its expected value? If required, round your answer to one decimal place. e. What is the expected value of perfect information? If required, round your answer to one decimal place.Please show how to solve b
- Solve the following decision tree using the EMV rule and state the optimal strategy. B C .25 D 35 E 40 F 2 G 8 20 -50 H J K M N R 180 50 S 55 T 45 U 25 V 35 W S X 5 Y 4 Z 6 AA 3 BB 4 CC 3 300 100 10 80 -30 120 500 --200 150 100 50c. Formulate Linear Optimization Models for the following: i. A company has been given a tender to supply maize to four drought zones. The cost of transporting each unit from the grains depot to the drought zone is given below: 1 | 2 | 3 4 Supply 1 21 16 25 | 13 17 18 14 23 13 3 32 27 18 41 19 Demand 10 12 15 43 6. 2.Problem 4-11 (Algorithmic) Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many units of each…
- GRAPHICAL METHOD: A store wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants which will sell for $30. Offer B is a package of three shirts and a pair of pants, which will sell for $50. The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B. How many packages of each do they have to sell to maximize the money generated from the promotion? Attach the PDF or JPEG file of the solution made. *Problem 2: You go to the racetrack and are choosing between 2 horses: Belle and Jeb (you are at the racetrack, so you will bet on one of these two horses). Betting on either horse will cost you $1, and the payoffs are as follows: • Bet on Belle: you will be paid $2 if she wins (or a net profit of $1). You believe she has a 75% chance of winning. • Bet on Jeb: you will be paid $9 if he wins (for a net profit of $8). You believe that he has a 20% chance of winning. Prior to making your decision of which horse to bet on, someone comes and offers you gambler’s “insurance.” If you agree to the gamblers “insurance,” they pay you $1 immediately and you agree to pay them 50% of the profit on your winnings (that is, $0.50 if Belle wins, and $4 if Jeb wins). What should you do? Answer this question by: a) Creating a decision tree for this scenario, making sure you label all branches and include all probabilities and consequences. b) Solving the decision tree using EMV and stating the optimal…Problem 3-19 (Algorithmic) Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated…