Concept explainers
To explain: A linear programming that has feasible region with infinite number of solutions.
Introduction:
Linear programming:
It is a linear optimization technique followed to develop a best outcome for the problem in hand. The outcome might be of maximum profit or less cost which are represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.
Feasible region:
A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.
Trending nowThis is a popular solution!
Chapter B Solutions
Operations Management: Sustainability and Supply Chain Management (12th Edition)
- If a "Prisoner’s Dilemma" type of game is played repeatedly for a given number of finite periods that is known to each player, players can maintain cooperation throughout the game. true or false? Solve this Economicarrow_forwardDiscuss several advantages of linear programming; clearly explain the reasons for your choices.arrow_forwardFormulate a system of equations for the situation below and solve. Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 18%/year, while the bonds and the money market account pay 12%/year and 6%/year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. How should the Garcias allocate their resources if they require an annual income of $15,000 from their investments? stocks $ bonds $ money market $arrow_forward
- Discuss several disadvantages of linear programming; clearly explain the reasons for your choices.arrow_forwardProblem 2: Applications of Linear Programming: Visa Inc. Stock sells for $92 a share and has 3-year average annual return of $20 a share. The beta value is 1.06. JP Morgan Chase and Co. sells for $87 a share and has a 3-year average annual return of $17 a share. The beta value is 1.21. Derek wants to spend no more than $15,000 investing in these two stocks, but he wants to earn at least $2500 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.arrow_forwardBugs Bunny and Daffy Duck are contestants on a game show called Split or Steal. On the show, Bugs and Daffy have to pick one of two cards and decide to split the prize money of $100,000 or steal it from the other contestant. The decisions are made simultaneously so neither player knows what the other will do. The table below represents the result of the contestants’ choices. See attached What should a rational player do in this game? Is this a zero-sum game?arrow_forward
- For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.arrow_forwardI need solve this please fastarrow_forwardLarry just received a fund of $177,000 from selling his property in Utica. He wants to invest this fund and is considering investing on these four possible investment options: a technology stock, a healthcare stock, a mutual fund, and a one-year certificate of deposit (CD). Larry estimates the return on the technology stock to be about 7.15% and the healthcare stock to be 10.55%. The mutual fund has a return rate of 11%. The CD has a 5% return rate. To diversify his investment, Larry would like the following setups for his investment: 1) At least $35,000 must be invested in CD. 2) The combined investment on the two stocks (technology and healthcare) cannot be more than $115,000 3) No more than $55,000 should be invested in the mutual fund. 4) The investment on the technology stock should be no more than the investment on the healthcare stock Like most investors, Larry wants to maximize the return of his investment. Set up a linear program to help Larry with his investment decision.…arrow_forward
- Problem 7-25 (Algorithmic) George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 9% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 60% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 8.5%. a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = percentage of funds invested in the bond fund S percentage of funds invested in the stock fund s.t. Optimal solution: B = Value of optimal solution is S = B + % B B…arrow_forwardLindsey Brentwood is the manager of a fine dining restaurant chain that serves its guests a variety of traditional Southern dishes prepared with the very finest of ingredients. It is most famous for its upscale version of Chicken Fried Steak. At Lindsey's restaurant, this dish (beef steak, seasoned, breaded, and then pan fried) is prepared using USDA Prime rib-eye steak. As the price of rib-eye has increased, Lindsey’s food cost percentage on this item has risen dramatically. Currently, Lindsey is considering whether the selling price of this dish should be increased significantly or if she should take other steps to help reduce her overall product cost percentage. 1. What issues should Lindsey consider prior to making this decision? 2. What alternatives to raising prices do you think are available to Lindsey?arrow_forwardProblem 7-25 (Algorithmic) George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 6.5%. a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = S Max s.t. percentage of funds invested in the bond fund percentage of funds invested in the stock fund Optimal solution: B Value of optimal solution is X X,S= B X…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,Operations ManagementOperations ManagementISBN:9781259667473Author:William J StevensonPublisher:McGraw-Hill EducationOperations and Supply Chain Management (Mcgraw-hi...Operations ManagementISBN:9781259666100Author:F. Robert Jacobs, Richard B ChasePublisher:McGraw-Hill Education
- Purchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage LearningProduction and Operations Analysis, Seventh Editi...Operations ManagementISBN:9781478623069Author:Steven Nahmias, Tava Lennon OlsenPublisher:Waveland Press, Inc.