There are six projects represented by 0-1 variables X1, X2, X3, X4, X5 and X6. Write a constraint modelling for the following capital budgeting problem. a) Two of the projects 1, 3, 5 and 6 must be undertaken. b) If projects 3 and 5 must be undertaken, they must be undertaken simultaneously. c) Project 1 or 4 must be undertaken, but not both.

There are six projects represented by 0-1 variables X1, X2, X3, X4, X5 and X6. Write a constraint modelling for the following capital budgeting problem. a) Two of the projects 1, 3, 5 and 6 must be undertaken. b) If projects 3 and 5 must be undertaken, they must be undertaken simultaneously. c) Project 1 or 4 must be undertaken, but not both.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 39P

See similar textbooks

Similar questions

A linear programming computer package is needed. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 42 30 Hours required to complete all the cherry cabinets 60 48 35 Hours available 40 30 35 Cost per hour $36 $42 $55 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours…
3. Elana owns a consulting business that helps software companies market their services to school districts. She earns an average of $4635.7 for every contract one of her client companies signs with her help. In order to be able to run her business, she needs to cover $7,000/month (rent, licenses, etc.). The average costs associated with each contract are $1676.6. How many contracts must she facilitate each month in order to break even? a. -2.37 b. 2.37 c. 10966.14 d. 1.51 e. -1675.09 f. None of the other options.
4. Ana owns a consulting business that helps software companies market their services to school districts. She earns an average of $4635.7 for every contract one of her client companies signs with her help. In order to be able to run her business, she needs to cover $7,000/month (rent, licenses, etc.). The average costs associated with each contract are $1676.6. How many contracts must she facilitate each month in order to break even? a. 2.37 b. 1.51 c. -2.37 d. -1675.09 e. 10966.14 f. None of the other options.
Which of the folowing linear programming model has an unbounded feasible region? = 3x + 2y subject to the following : O max z x+ y34 *< 10 – 4y x20 y20 O None of the above O max z = 3x + 2y subject to the following : x+ 2y <4 x- ys1 x20 y20 O max z = 4x +2y subject to the following : x + 2y 24 3x + y27 -x + 2y s7 x20 y20
Michael has decided to invest $40,000 in three types of funds. Fund A has projected an annual return of 8 percent, Fund B has projected an annual return of 10 percent, and Fund C has projected an annual return of 9 percent. He has decided to invest no more than 30 percent of the total amount in Fund B and no more than 40 percent of the total amount in Fund C. a. Formulate a linear programming model that can be used to determine the amount of investments Michael should allocate to each type of fund to maximize the total annual return.b. How much should be allocated to each type of fund? What is the total annual return?
(a) Mary is planning to do two part-time jobs, one in the retail store ABC and the other in the restaurant LMNO, to earn tuition. She decides to earn at least $120 per week. In ABC, she can work 5 to 12 hours a week, and in LMNO, she can work 4 to 10 hours a week. The hourly wages of ABC and LMNO are $6 per hour and $8 per hour, respectively. When deciding how long to work in each place, Mary hopes to make a decision based on work stress. According to reviews on the Internet, Mary estimates that the stress levels of ABC and LMNO are 1 and 2 for each hour of working, respectively (stress levels are between 1 and 5; a large value means a high work stress which may cause work and life imbalance). Since stress accumulates over time, she assumes that the total stress of working in any place is proportional to the number of hours she works in that place. How many hours should Mary work in each place per week? State verbally the objective, constraints and decision variables. Then formulate…
In the game shown below, Player 1 can move Up or Down, and Player 2 can move Left or Right. The players must move at the same time without knowledge of the other player’s move. The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Solve each game using game theoretic logic. Player 2 Player 1 Left Right Up 3, 2 2, 3 Down 0, 9 1, 1
Ana is a university student with 12 hours available daily, and she wants to distribute her time betweenstudy (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling heruniversity obligations. Ana considers leisure to be twice (2) as enjoyable as studying, but she alsobelieves that she should spend at least twice (2) as much time studying as she does on leisure activities.Additionally, she cannot spend more than five (5) hours a day on leisure activities to ensure that she hasenough time for her university obligations. 1. How much additional enjoyment would Ana get if she had one more hour per dayavailable, so 13 instead of 12 (dual price)?2. Would Ana experience a greater level of enjoyment if she allows herself to have amaximum of six hours per day to leisure activities instead of five, while still fulfilling her universityobligations within the 12 hours available (dual price)?3. What is the allowable increase of the coefficient accompanying leisure…
SUPPOSE THAT THE OPPORTUNITY COST OF A MINIMIZATION ASSIGNMENT PROBLEM BECOMES II IV A. 4 3 10 B 4 2 10 6 2 10 4 WHICH OF THE FOLLOWING GIVES AN OPTIMAL ASSIGNMENT? A is assigned to IV Bis assigned to II Cis assigned to I Dis assigned to II No optimal assignment is possible yet. O A is assigned to lII Bis assigned to IV Cis assigned tol Dis assigned to II O A is assigned to l Bis assigned to IV Cis assigned to II Dis assigned to II
Problem: A bicycle shop Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming season. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20, $67 if they order 40, $65 if they order 60, and $64 if they order 80. The bicycles will be sold for $100 each. Any bicycles left over at the end of the season can be sold (for certain) at $45 each. If Zed and Adrian run out of bicycles during the season, then they will suffer a loss of "goodwill" among their customers. They estimate this goodwill loss to be $5 per customer who was unable to buy a bicycle. Zed and Adrian estimate that the demand for bicycles this season will be 10, 30, 50, or 70 bicycles with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively. Instruction: Given the problem below "The Bicycle Shop" Provide the correct answers with solutions of the following: a. Payoff Table b. Opportunistic Loss Table c. Expected…
7. The following questions refer to a capital budgeting problem with six projects represented by 0-1 variables x1, X2, X3, X4, X5, and x6: a. Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken. b. Write a constraint modeling a situation in which, if projects 3 and 5 must be undertaken, they must be undertaken simultaneously. C. Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both. d. Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 also are undertaken. e. In addition to the requirement in part (d), assume that when projects 1 and 3 are undertaken, project 4 also must be undertaken.
Problem 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.