Can you please solve the linear equation graphically with clear steps
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Can you please solve the linear equation graphically with clear steps
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- 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 0Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 7 x1 + 3 x2 ≥ 21 (2) x1 + 3 x2 ≥ 6 Group of answer choices (x1, x2) = (2, 5) (x1, x2) = (1, 2) (x1, x2) = (0, 4) (x1, x2) = (0.5, 5)1. Consider the following linear programming formulation: Min 5x + 2y Subject to (1) 3x + 6y ≥ 18 (2) 5x + 4y ≥ 20 (3) 8x + 2y ≥ 16 (4) 7x + 6y ≤ 42 (5) x, y ≥ 0 a. Solve the problem graphically. Specifically, show each constraint and the feasible region, draw an objective function line and identify an optimal point (the solution). When reporting the optimal solution and the corresponding objective function value, you may estimate the optimal x and y values from the graph. b. What are the optimal values of x and y, using the solver add-in? What is the corresponding value of the objective function? c. How many extreme points does the feasible region have? Enumerate them. Hint: It's from the graph. d. Change the objective function to 15x + 12y.. What is the new optimal solution(s)?
- 4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.Determine whether the problem has multiple solutions, unbounded solutions, or no feasible solutions.Maximize z = 10x1 + 11x2 + 7x3, subject to 2x1 + 3x2 − 9x3 ≤ 72 2x1 + 5x2 − 10x3 ≥ 100 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 The problem has multiple solutions. The problem has unbounded solutions. T he problem has no feasible solutions.Consider the following set of constraints: 48Y >= 7296; 0.25 X + 12Y >= 1824, and X + Y <= 152. Pick a suitable statement for this problem: a. Solution to this problem cannot be found without the objective function. b. The feasible region is defined by a single (unique) point. c. It is a non-linear problem - unsuitable for grphical method. d. This problem has two feasible points - one is optimal for miniization problem and other is optimal for maximization problem. e. Feasible region is represented by a line and multiple feasible points are available.
- 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…(5) Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: _______________________________________________________________(c) Which of the following points yields the best solution? Underline the best solution: (7,5), (9,2), (6,6).Justify your answer (using the data from the above LP…Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________
- Consider the following LP problem with two constraints: 18X + 8Y >= 144and 9X + 4Y= 36. The objective function is Min 14X + 30Y . What combination of X and Y will yield the optimum solution for this problem? a. infeasible problem b. unbounded problem c. 0 , 9 d. 4 , 0 e. 2 , 4.521. 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)Which of the following could not be a constraint for a linear programming problem? Multiple Choice 1A + 2B = 3 1A + 2B 1A + 2B ≤ 3 1A + 2B ≥ 3 1A + 2B + 3C ≤ 3