(a) maximize subject to - 2x₁ + x₂ F₁-x₂ ≤ 1, 2x1 - x₂ ≥ 1, 2x1 + 2x₂ ≥ 4, I1, I2 20
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- Elaborate/ Explain Integer Linear Optimization and put examplesConsider 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 01. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.
- 3. (Note: This is a variation of problem 6 of chapter 16 in your textbook.) Kenya and Dionne live on adjacent plots of land. Each has two potential uses for their land, the present values of each of which depend on the use adopted by the other, as summarized in the table. All the values in the table are known to both parties. Dionne Rental housing Bee keeping Kenya Apple growing A: $200 B: $700 A: $400 B: $650 Pig farming A: $450 B: $400 A: $450 B: $500 a. What is the efficient outcome? b. If there are negotiation costs of $150, what activities will the two pursue on their land? c. If there are no negotiation costs and the two negotiate, what activities will the two pursue on their land? How might a benevolent planner help reduce the costs of negotiating to encourage the optimal combination of land uses?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.WHAT WLL HAPPEN IF THERE IS A CHANGE IS ONE OF THE OBJECTIVE FUNCTION COEFFICIENT? A. SLOPE OF THE OBJECTIVE FUNCTION LINE ALWAYS WILL CHANGE B. OPTIMAL SOLUTION ALWAYS WILL CHANGE C. ONE OR MORE OF THE DECISION VARIABLES ALWAYS WILL CHANGE D. ALL OF THE ABOVE E. NONE OF THE ABOVE
- (b) Indicate whether the following linear program is an all-integer linear program or a mixed-integer linear program. Max 3x1 + 4x2 s.t. 2x1 + 4x2 2 8> 2x1 + 6x2 2 12 x1, x2 2 0 and integer This is a Max s.t. Write the LP Relaxation for the problem but do not attempt to solve. If required, round your answers to one decimal place. Its LP Relaxation is 2x1 + x1, x2 linear program. xz x1 + 6x21Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10
- 9.5 Capital Healthplans Inc. is evaluating two different methods for providing home health services to its members. Both methods involve contracting out for services, and the health outcomes and revenues are not affected by the method chosen. Therefore, the net cash flows for the decision are all outflows. Here are the projected flows: Year Method A ($) Method B ($) 0 (300,000) (120,000) 1 (66,000) (96,000) 2 (66,000) (96,000) 3 (66,000) (96,000) 4 (66,000) (96,000) 5 (66,000) (96,000) What is each alternative’s IRR? If the opportunity cost of capital for both methods is 9 percent, which method should be chosen? Why?(c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2 units of raw material 1, 6 units of raw material 2 and 4 units of raw material 3. Product Y costs $10 per unit and contains 2 units of raw material 1, 2 units of raw material 2 and 12 units of raw material 3. The company has 80 units of raw material 1, 120 units of raw material 2 and 240 units of raw material 3 available. In addition, the product Y should be at least 15 units less than product X. How many units of each product should the company produce to minimize the cost of production? (i) (ii) Derive the system of equations. Use the extreme point method to solve the system. Ensure that you explain each step in the computation.1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?