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- 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.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 = 53) A brokerage firm has been tasked with investing $500,000 for a new client. The client has asked that the broker select promising stocks and bonds for investment, subject to the following guidelines: at least 20% in municipal bonds, at least 10% each in real estate and pharmaceutical stock, and at least 40% in a combination of energy and domestic automobile stocks with each accounting for at least 15%. The returns are as follows: Municipal = 5.3%, Domestic Automobile = 8.8%, Energy = 4.9%, Pharmaceuticals = 8.4% and Real Estate = 10.4%. a) Write a linear program complete with objective function and all constraints to Maximize the return. (5 points) b) What is the optimal solution? Give values for all variables rounded to the nearest cent.(2 points) c) How much annual income does the optimal solution generate? (2 points) d) Submit your excel workbook. (2 points)
- 2. As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs $10,000 and each training program on problem solving costs $8000. a. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem solving that should be offered in order to minimize total cost. b. Determine the optimal…1. How is linear programming used in real-world applications? expand the answer.Second consulting is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and support personnel required for each project, and the expected profits for each project are summarized in the following table: Project 1 2 3 4 5 6 Engineers required 20 55 47 38 90 63 Support personnel required 15 45 50 40 70 70 Profit ($1,000,000s) 1.0 1.8 2.0 1.5 3.6 2.2 There are 175 engineers available and 150 support personnel available for these projects. Further, no more than 3 projects can be done. Formulate an integer program to solve this problem. Define the decision variables needed to model this problem. The objective is to maximize profit. Give the objection function. Write the constraints. What is the final answer? Explain in detail.
- Consider the following linear program. Max 1A + 2B s.t 1A≤ 4 1B≤ 3 2A + 2B = 10 A, B ≥ 0 (a) Show the feasible region. (b) What are the extreme points of the feasible region? (b) What are the extreme points of the feasible region? smaller x-value (A, B) = (______) larger x-value (A,B)= (_____) (c) Find the optimal solution using the graphical procedure. (A, B) = (______)ProFood Supply Company This case revolves around the issue of sales strategy. Jon is faced with two alternative sales strategies for trying to make his sales quota. Neither appears to be a good short term solution. Summary ProFood Supply Company, founded in New York in 1960, has grown steadily over the decades to become one of the largest full-service institutional food suppliers in the nation, selling perishable and non-perishable foods and foodservice supplies such as tablecloths, napkins, and tableware. In the past year, ProFood had begun an aggressive push into a new market segment, the hotel/motel restaurant market. Jon Menzes, the ProFood sales representative in Nashville, Tennessee, has been with the company for two years and hopes to move into management someday. His sales manager, Emily Lewis, told him that if he finished the year over 100% of his sales versus quota that he would be put into the pool of candidates considered for a promotion during the next twelve months. To…Issue 1 (name the issue) Issue 1 Description. Describe the issue. Explain why it is an issue. Issue 1 Solution (description). Describe your solution to the issue above Issue 1 Advantages and disadvantages (description). Explain the advantages and disadvantages of your solution. In this section disadvantages should not outweigh the advantages. Issue 2 (name the issue) Issue 2 Description. Describe the issue. Explain why it is an issue. Issue 2 Solution (description). Describe your solution to the issue above Issue 2 Advantages and disadvantages (description). Explain the advantages and disadvantages of your solution. In this section disadvantages should not outweigh the advantages.
- May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file. An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Return Maximum Allowed Low-income mortgage loans 6.50% 20% Conventional mortgage loans 6.00% 30% Government sponsored mortgage loans 8.25% 25% Bond investments 5.75% 15% Stock investments 8.75% 18% Futures trading 9.25% 10%Manny Billard Real Estate Company has PHP 2 million available for the purchase of new rental property. After an initial screening, Billard reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for PHP 282,000, and five are available. Each apartment building can be purchased for PHP 400,000, and the developer will construct as many buildings as Billard wants to purchase. Billard property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be PHP10,000 per townhouse and PHP15,000 per apartment building. How many townhouses would have left (unpurchased) if Billard will go for the optimal solution?