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.
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)21. A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? Part 2 A. The graphical origin (0, 0) is not in the feasible region. B. The feasible region includes all points that satisfy one constraint, the other, or both. C. The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. D. The two corner points are (0, 0) and (50, 12.5). E. There are four corner points including (50, 0) and (0, 12.5)11. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization LP problem, this means: a. if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 5 b. if the RHS for that constraint is increased by one then the optimal objective function value is increase by 5 c. if the RHS for that constraint is increased by 5 then the optimal objective function value is increase by 1 d. if the coefficient of the objective function is increase by 5 then the RHS for that constraint must be increased by 1 12. Sensitivity Analysis generally assumes a. we are considering a change in two input data values at a time b. are considering a change in only one input data value at a time c. we are considering several change in several input data…
- 22. Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn? Part 2 A. $10 B. $0 C. $14 D. $21 E. $15Consider 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 0Consider the following LP problem: Min 6X+ 18Y; Subject to : 3 X + 9Y <= 47, and X + Y <= 141. Which one of the following is true?: a. Slack for each constraint is zero. b. Optimal Obj. function value is 94 c. X=70.5, Y=70.5 is the only optimal solution. d. Optimal Obj. function value is 0
- 1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to x1 + x2 >= 40 x1 + 4x2 >= 60 3x1 + x2 >= 60 x1 >= 0, x2 >= 0 a. Solve the LP model graphically and explain the solution result. b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution? 2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic…A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 780, 900, and 720, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. ProductA ProductB ProductC Dept. I 2 1 2 Dept. II 3 1 2 Dept. II 2 2 1 Profit $18 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A product B product C What is the maximum profit (in dollars)?The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
- 2 ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware, and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops. Instructions: If the spreadsheet and Excel Solver results are given to you as follows (see Table 1 below), address the following questions: What are your Binding Constraints? What is your Optimum profit [hint: maximized profit]? What are your slack values for Pine, Oak, and Labor? Looking at the Shadow prices, how much would the objective profit increase by if you were to…The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from five departments: Dept. 1 Dept. 2 Dept. 3 Dept. 4 Dept. 5 $450,000 $310,000 $275,000 $187,500 $135,000 Because the total budget requests exceed the available $1.2 million, not all the requests can be satisfied. Suppose the CFO wants to make sure each department receives at least 70% of the requested amount. Further, suppose the CFO considers the requests for departments 2 and 3 to be twice as important as those from departments 4 and 5, and the request from department 1 to be twice as important as those from departments 2 and 3. The CFO want to minimize the sum of the weighted deviations from the goals. What is the optimal sum of weighted deviations? a. 0.96 b. 1.00 c. 0.00 d. 218.25A. What is the optimal solution and what is the optimal value of the objective function? B. Which constraints are binding? C. What are the dual values? Interpret each. D. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why?