Given the following linear optimization problem
Given the following linear optimization problem
Maximize 10x + 20y
Subject to
x+y ≤ 50
2x + 3y ≤ 120
X ≥ 10
X,y≥0
(a) Graph the constraints and determine the feasible region.
(b) Find the coordinates of each corner point of the feasible region
(c) Determine the optimal solution and optimal objective function value.
Homework Answers
3. Consider the following linear programming problem: Maximize 10X + 12Y Subject to: 8X + 4Y...
3. Consider the following linear programming problem: Maximize 10X + 12Y Subject to: 8X + 4Y ≤ 840 2X + 4Y ≤ 240 X, Y ≥ 0 Graph the constraints and shade the area that represents the feasible region. Find the solution to the problem using either the corner point method or the isoprofit method. What is the maximum feasible value of the objective function?
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution...
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution exists at a single vertex point. b. There is more than one optimal solution. C. There is no optimal solution because the feasible region does not exist d. There is no optimal solution because the feasible region is unbounded. Maximize: 2x +3y Subject to: x +2y 28 5. Graph the inequality: 2x +3y >12 6. Graph the system of inequalities: 7. Graph the system...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i...
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
Feasible region for an optimization problem is given as follows: у D E B A X...
Feasible region for an optimization problem is given as follows: у D E B A X Coordinates of the corner points are given in below table: Corner Points A B с D E Coordinates X 4 2 8 3 7 6 5 8 5 Find the optimum values of the following objective functions according to the given feasible region: a) min z = 5x +9y b) min z = 2x – 3y c) max z = 3x + 4y max...
Solve the following linear programming problem graphically:
Solve the following linear programming problem graphically: Maximize Z=4X₁+4X₂, Subject to: 3X₁ + 5X₂ ≤ 150 X₁ - 2X₂ ≤ 10 5X₁ + 3X₂ ≤ 150 X₁, X₂ ≥ 0 1) Using the line drawing tool, plot the constraints by picking two endpoints for each line. Do not plot the nonnegativity constraints. 2) Using the point drawing tool, plot the five corner points which define the feasible region. The optimal solution is X₁ = _______ and X₂ = _______ (round your responses to two decimal places). Maximum profit is $_______
3. Consider the linear programming problem with objective function Q = 4x – 3y and constraints:...
3. Consider the linear programming problem with objective function Q = 4x – 3y and constraints: 9x + 4y > 180, 3x + 8y > 120, 0 < x < 35, y > 0. Graph all constraints and show the feasible region and all corner points. Can the objective function be maximized? If so, find the maximum value of Q.
Solve by Linear Programming. (Be sure to show the graph of the feasible region, the appropriate...
Solve by Linear Programming. (Be sure to show the graph of the feasible region, the appropriate vertices, optimal value, AND SHOW ALL WORK!.) Exercise 1 LP 1. Maximize: C = x – y Constraints: x ≥ 0, and y ≥ 0 x + 3y ≤ 120 3x + y ≤ 120 Exercise 2 LP 2. Maximize: C = 3x + 4y Constraints: x + y ≤ 10 – x + y ≤ 5 2x + 4y ≤ 32
1. Is the following linear optimization problem infeasible, unbounded, or has multiple optimal solutions? Draw a...
1. Is the following linear optimization problem infeasible, unbounded, or has multiple optimal solutions? Draw a graph and explain. Minimize 40x + 25y Subject to 2x + 3y > 45 x + y < 10 x, y > 0
4. (hand solution) Use the graphical approach of linear programming to solve this problem; draw a graph and identify the feasible region Maximize f (x, y) = 10x-Sy subject to 4. (hand solution)...
4. (hand solution) Use the graphical approach of linear programming to solve this problem; draw a graph and identify the feasible region Maximize f (x, y) = 10x-Sy subject to
4. (hand solution) Use the graphical approach of linear programming to solve this problem; draw a graph and identify the feasible region Maximize f (x, y) = 10x-Sy subject to
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution exists at a single vertex point. b. There is more than one optimal solution. C. There is no optimal solution because the feasible region does not exist d. There is no optimal solution because the feasible region is unbounded. Maximize: 2x +3y Subject to: x +2y 28 5. Graph the inequality: 2x +3y >12 6. Graph the system of inequalities: 7. Graph the system...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
Feasible region for an optimization problem is given as follows: у D E B A X Coordinates of the corner points are given in below table: Corner Points A B с D E Coordinates X 4 2 8 3 7 6 5 8 5 Find the optimum values of the following objective functions according to the given feasible region: a) min z = 5x +9y b) min z = 2x – 3y c) max z = 3x + 4y max...
3. Consider the linear programming problem with objective function Q = 4x – 3y and constraints: 9x + 4y > 180, 3x + 8y > 120, 0 < x < 35, y > 0. Graph all constraints and show the feasible region and all corner points. Can the objective function be maximized? If so, find the maximum value of Q.
4. (hand solution) Use the graphical approach of linear programming to solve this problem; draw a graph and identify the feasible region Maximize f (x, y) = 10x-Sy subject to
4. (hand solution) Use the graphical approach of linear programming to solve this problem; draw a graph and identify the feasible region Maximize f (x, y) = 10x-Sy subject to
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