11. Refer to Problem 10 and the computer solution shown in Figure 3.16. a. Suppose the risk index for the stock fund (the value of Cs) increases from its current value of 8 to 12. How does the optimal solution change, if at all? b. Suppose the risk index for the money market fund (the value of CM) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all? c. Suppose Cs increases to 12 and CM increases to 3.5. How does the optimal solution change, if at all?
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- 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…1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????
- 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. $15Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 01. Discuss the positive impact of ICT in education and Business 2. Highlight the negative impact of ICT in education and Business 3. A company is considering a R250 000 investment with the following cash flows Year 1 : R30 000 Year 2: R60 000 Year 3: R120 000 Year 4: R130 000 Year 5: R160 000 a) Determine the payback period of the investment ( present in table format) b) If the company wants to recover its initial investment in year 3, is the investment worthwhile? c) Identify and explain any 3 advantages of using payback method.
- Mr. Barrera raises goats and pigs. He wants to raise no more than 16 animals including no more than 10 goats. It will cost $25 to raise each goat and $75 to raise each pig. She will make $12 in profit from each goat and $40 in profit from each pig. She has $900 to raise animals. How many of each type of animal should she raise to maximize profit?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…Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…
- INCORRECT FORFormulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. (Let BR = pounds of Brazilian beans purchased to produce Regular, BD = pounds of Brazilian beans purchased to produce DeCaf, CR = pounds of Colombian beans purchased to produce Regular, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max 2.033BR+2.582BD+1.868CR+2.418CD INCORRECT Pounds of Regular BR+CR≤900 INCORRECT Pounds of DeCaf BD+CD≤400 INCORRECTA goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.Suppose an assignment problem, where there are 3 employees who must perform 3 different tasks. The times (in hours) that employees take to perform each of the tasks is shown below. Each employee must perform only one task, and a task can only be performed by one employee. All employees are paid exactly the same wage per hour of work. Minimize the total time to make all tasks. Task 1 Task 2 Task 3 Employee 1 154 29 40 Employee 2 18 137 12 Employee 3 94 13 31 How many variables does the problem have? How many constraints does the problem have? The objective function corresponds to: