Estimate a range for the optimal objective value for the following LPs: (a) Minimize z = 5x₁ + 2x₂ subject to (b) Maximize z = x₁ + 5x₂ + 3x3 subject to x₁ - x₂ = 3 2x₁ + 3x₂ = 5 X1, X₂ = 0 x₁ + 2x₂ + x3 = 30 2x₁ - x₂ = 40 X1, X₂, X3 ≥ 0
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- 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 - 3x2LPP 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 )Graph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10A 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 solution
- Describe the analysis of simultaneous changes in coefficients of objective function??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 0Ian Langella faces a decision how large his gasoline station should be. The annual returns wil l depend on both the size of his station and number of marketing factors related to the oil in dustry and demand for gasoline. Ian develop a careful analysis based on the following table: Size of first station Market condition Market conditon Market conditon Good Fair Poor Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000 Develop a decision table for this decision
- Q1 Find the best solution for the following model using simplex MAX Z = 10X1 + 8X2 SUB TO: 4X1 + 2X2 < 80 X1 + 2X2 < 50 X1 2 0,X2 2 0Determine 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 OChikana Company produces and sells rattan baskets. The number of drifts produced are the corresponding total production costs for six months, which are representatives for the year, are as follows: Month Units Produced Production Costs P 4,000 8,000 6,000 7,500 8,500 7,250 April Мay 500 700 June 900 July August September 600 800 550 Required: Solve for the variable and fixed cost component using: a.) High- Low Method b.) Least- Squares Regression