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?
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3. Consider the following linear programming problem: Maximize
10X + 12Y Subject to: 8X + 4Y...
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.
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
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?
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y...
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y = 10 6x + y s 10 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Use graphical methods to solve the following linear programming problem. Maximize: z= 3x + y subject...
Use graphical methods to solve the following linear programming problem. Maximize: z= 3x + y subject to: x-ys7 3x + 5y = 45 X20, y20 Graph the feasible region using the graphing tool to the right. Click to enlarge graph , at the corner point The maximum value of z is (Simplify your answers.) of T o to 12 14 16
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.
Find the values of x2 0 and y 2 0 that maximize z 10x+ 12y, subject to each of the following sets of constraints (a) x...
Find the values of x2 0 and y 2 0 that maximize z 10x+ 12y, subject to each of the following sets of constraints (a) x ys 13 x +4y s 16 (b) x 3y 2 12 3x y2 18 (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The maximum value occurs at .(Type an ordered pair.) 0 B. There is no maximum value.
Find the values of x2...
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 $_______
Solve the linear programming problem by the simplex method. Maximize P = 5x + 4y subject...
Solve the linear programming problem by the simplex method. Maximize P = 5x + 4y subject to 3x + 5y 78 4x + y 36 x 0, y 0 x = y = P =
Solve the following linear programming problem. Maximize: z = 4x + 10y subject to: 3x +...
Solve the following linear programming problem. Maximize: z = 4x + 10y subject to: 3x + 4y = 12 6x + y = 12 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
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
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?
Solve the following linear programming problem. Maximize: z= 3x + 4y subject to: 2x + 5y = 10 6x + y s 10 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
Use graphical methods to solve the following linear programming problem. Maximize: z= 3x + y subject to: x-ys7 3x + 5y = 45 X20, y20 Graph the feasible region using the graphing tool to the right. Click to enlarge graph , at the corner point The maximum value of z is (Simplify your answers.) of T o to 12 14 16
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.
Find the values of x2 0 and y 2 0 that maximize z 10x+ 12y, subject to each of the following sets of constraints (a) x ys 13 x +4y s 16 (b) x 3y 2 12 3x y2 18 (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The maximum value occurs at .(Type an ordered pair.) 0 B. There is no maximum value.
Find the values of x2...
Solve the following linear programming problem. Maximize: z = 4x + 10y subject to: 3x + 4y = 12 6x + y = 12 X20, y20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
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