Given the linear program Max 3x+4y S.T. -x+2y/=0 A. Write the problem in standard form. Identify slack/surplus variables. B. Find all the extreme points. List the value for x and y at each extreme point. C. What is the optimal solution? D. What are the values of the slack/surplus variables at the optimal solution?
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- Given the linear program
Max 3x+4y
S.T. -x+2y</=8
x+2y</=12
2x+y</= 16
x,y>/=0
A. Write the problem in standard form. Identify slack/surplus variables.
B. Find all the extreme points. List the value for x and y at each extreme point.
C. What is the optimal solution?
D. What are the values of the slack/surplus variables at the optimal solution?
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- When you use a RISKSIMTABLE function for a decision variable, such as the order quantity in the Walton model, explain how this provides a fair comparison across the different values tested.STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700
- What is the fertilizer constraint? a. 2r t c <= 10 b. r + c <= 10 c. 3r + 3c <= 10 d. none of the above19. 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 = 5WHAT WLL HAPPEN IF THERE IS A CHANGE IS ONE OF THE OBJECTIVE FUNCTION COEFFICIENT? A. SLOPE OF THE OBJECTIVE FUNCTION LINE ALWAYS WILL CHANGE B. OPTIMAL SOLUTION ALWAYS WILL CHANGE C. ONE OR MORE OF THE DECISION VARIABLES ALWAYS WILL CHANGE D. ALL OF THE ABOVE E. NONE OF THE ABOVE
- 1. Construct a 2-by2 contingency table to determine the total number of people who fail the screening test and will be referred for diagnostic testing in the hearing centers. 2. Construct a 2-by-2 contingency table to determine the total number of people who fail the diagnostic test, which represents the target market for hearing aid sales.Minimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0LPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )
- Q1. Build a linear programming model to develop an investment portfolio that minimizes total risk under the above constraints. a) Define the decision making variables. b) Show the objective function. c) Show the constraints. Q2. What is the optimal solution and what is the value of the objective function? Show the relevant portion of the Solver’s output. Fully interpret the results. Q3. What are the objective coefficient ranges for the four stocks? Show the relevant portion of the Solver’s output. Fully interpret these ranges. Q4. Suppose the investor decides that the annual rate of return no longer has to be at least 9% and agrees to at minimum level of 8%. What does the shadow price associated with this constraint indicate about a possible change in total risk that could occur from this lower rate of return? Show the relevant portion of the Solver’s output. Fully interpret the results.Consider Bruno who manages an underwriting team in an insurance firm. Recently, the management of Bruno’s firm informed him of their decision to create a new risk assessment team, consisting of data scientists with machine learning expertise, and reduce the size of Bruno’s underwriting team. Bruno’s underwriting team will now work with the new risk assessment team in order to determine whether to provide insurance to applicants Use the model of a firm’s technology choice and graphically illustrate the management’s restructuring decision in a diagram with isocost curves. Your diagram should have the amount of human intelligence on the horizontal axis and the amount of artificial intelligence on the vertical axis. Fully label your diagram. Note that there are no actual numbers given in this question: you may make them up or simply use appropriate notations. Briefly explain the key information of your diagram.Consider the following linear programming problem Max. Z = 9X₁ + 16X₂ Subject to: C1: C2: C3: C4: C5: Variable Cells X₁ 2X₁ X₁ X₁ Microsoft Excel 16.0 Sensitivity Report Worksheet: [Question Sensitivity analysis.xlsx]Sheet2 Report Created: 10/24/2021 10:45:53 AM $B$5 Values x1 $C$5 Values x2 $D$10 C5Z $D$6 C1Z $D$7 C2Z $D$8 C3Z $D$9 CAZ X₂ This problem was solved using MS Solver of MS Excel. Following is the output of the solution. 3 6 3X₂ 0 0 X₂ Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease 6 3 24 9 3 Constraints Cell Name Value Price R.H. Side 05500 -5 5 15 3 0 0 0 3 24 10 0 Final Shadow Constraint Allowable Allowable Increase Decrease 1E+30 5 1E+30 24 10 6 3 3 1E+30 1E+30 7.5 3 18 1 3 1E+30 Write your report on the sensitivity analysis of constraints C2 and C3