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- A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solutionminimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2WHAT 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
- Consider 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 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 )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: 3
- Graph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=Indicate which of the following is an all-integer linear program and which is a mixed-integer linear program. Write the LP Relaxation for the problem but do not attempt to solve. (a) 70x1 + 65x2 (b) Is this linear program an all-integer linear program or a mixed-integer linear program? This is an all-integer linear program. This is a mixed-integer linear program. Max Write the LP Relaxation for the problem. s.t. (1) (2) (3) Max s.t. ---Select--- (1) 9x₁ + 4.5x₂ ≤ 400 (2) 4.5X₁ + 2x₂ ≤250 (3) x₁ + x₂ ≤ 150 X₁, X₂20 and X₂ integer Min s.t. (1) Is this linear program an all-integer linear program or a mixed-integer linear program? This is an all-integer linear program. This is a mixed-integer linear program. (2) Min s.t. Write the LP Relaxation for the problem. 7x1 + 8x2 (1) 6X₁ + 8X₂ ≥ 8 (2) 6X₁ + 10x₂ ≥ 12 X₁, X₂20 and integer ---Select---
- 4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O OConsider the following nonlinear program. max x(y – 2) s.t. x = 33 - 3y y 2 2 (a) (b) Derive the KKT necessary conditions for the nonlinear Solve the nonlinear program using the KKT necessary conditions. program.