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- 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…3. The Captain of a Cricket team has to allot 5 middle position to 5 batsmen. The average runs scored by each batsman at these positions are as follows Batting Positions III Batsmen II IV V P 40 40 35 25 50 27 50 42 30 16 25 R. 50 48 40 60 20 19 20 18 25 T 58 60 59 55 Find the assignment of batsmen to positions, which would give the maximum number of runs. If another batsman 'U' with the following average runs in batting positions as given below: Batting Positions: Average Runs: Is added to the team, should he be added to play in the team? If so, who should be replaced by him? II II IV V 45 52 38 50 49Four 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 1 699 445
- 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 =…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, 20Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)
- 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 = 850 − .1xwherey = Insurance needed ($000)x = Current age of head of household a. Plot the relationship on a graph. b. Use the equation to determine the amount of term life insurance to recommend for a family of four if the head of the household is 30 years old.Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex methodA 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 5,000
- Please show how to solve bexample 1a 1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0