20) The next table shows a cost matrix for an assignment problem. The optimal assignme be worker 1 3 worker 2 2 6 3 1 3 2 4 worker 3 worker 4 6. job 1 job 2 job 3 job 4 e) Z=6 f) Z=9 g) Z=11 h) Z=5 4) 2) 3.
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- ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5Minimize Z = 2x1 - 2x2 + 3x3, subject to - x1 + x2 + x3 ≤ 4 (resource 1) 2x1 - x2 + x3 ≤ 2 (resource 2) x1 + x2 + 3x3 ≤ 12 (resource 3) x1 , x2 , x3 are non-negative (a) Work through the simplex method step by step to solve the problem. (b) Identify the shadow prices for the three resources and describe their significance
- Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…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 ≤ x4Ann and Ben are getting divorced and want todetermine how to divide their joint property: retirementaccount, home, summer cottage, investments, and miscellaneous assets. To begin, Ann and Ben are told to allocate100 total points to the assets. Their allocation is as shownin Table 69.Assuming that all assets are divisible (that is, a fractionof each asset may be given to each person), how should theassets be allocated? Two criteria should govern the asset allocation:Criteria 1 Each person should end up with the same number of points. This prevents Ann from envying Ben and Benfrom envying Ann.Criteria 2 The total number of points received by Ann andBen should be maximized.If assets could not be split between people, what problemarises? TAB LE 69PointsItem Ann’s Ben’sRetirement account 50 40Home 20 30Summer cottage 15 10Investments 10 10Miscellaneous 5 10
- For a table manufacturing company, selling price for a table is $183.00 per Unit, Variable cost is $25.00 per Unit, rent is $3,380.00 per month and insurance is $296.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $254.00 per Unit, Variable cost to $43.00 per Unit, bigger area will have rent $5,235.00 per month and insurance is $362.00 per month At what point will the company be indifferent between the current mode of operation and the new option?Consider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.Answer the 3 subparts in 2 sentences each. For each of the following scenarios, please identify the most appropriate Operations Research model. RPI is facilitating a mentorship program and wants to assign undergraduate students with graduate student mentors. There are more undergraduate students than graduate students; therefore, each graduate student can be assigned at most 3 undergraduate student mentees. The goal is to maximize assignment satisfaction. The children’s game Snakes and Ladders is played in a sequential fashion. If a player is on a given square, the player can move to a different square based on selecting a card. This is a game of chance and there is no strategy in the game. The goal is predict who will win the game given the current location of both players. The US government wants to connect all major US cities with high-speed internet lines, which requires laying lines below ground. The US government wants to use the least amount of high-speed lines to connect…
- Answer the 3 subparts in 2 sentences each. For each of the following scenarios, please identify the most appropriate Operations Research model. RPI is facilitating a mentorship program and wants to assign undergraduate students with graduate student mentors. There are more undergraduate students than graduate students; therefore, each graduate student can be assigned at most 3 undergraduate student mentees. The goal is to maximize assignment satisfaction. The children’s game Snakes and Ladders is played in a sequential fashion. If a player is on a given square, the player can move to a different square based on selecting a card. This is a game of chance and there is no strategy in the game. The goal is predict who will win the game given the current location of both players. The US government wants to connect all major US cities with high-speed internet lines, which requires laying lines below ground. The US government wants to use the least amount of high-speed lines to connect…A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…Find the optimal solution to this linear programming problem. Min 3X+3Y s.t. 12X+4Y>=60 10X+5Y>=60 4X+8Y>=36 X,Y>=0 (X,Y) = ( )