3. Consider the linear programming problem with objective function Q = 4x – 3y and constraints:...
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?
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
Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1)...
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 $_______
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.
Graphical Method of Linear Programming 3. Find the minimum value of the objective function z = 5x + 7y, where x = 0 and y 0, subject to the constraints a. 2x + 3y 26 b. -x + y S4 c. 3x-y = 15 d. 2x + 5y = 27.
An objective function and a system of linear inequalities representing constraints are given. Complete parts a through c. Objective Function z = 4x-3y Constraints 25x56 y22 x-y2-4 a. Graph the system of inequalities representing the constraints. Use the graphing tool to graph the system. Click to enlarge graph b. Find the value of the objective function at each corner of the graphed region. (Use a comma to separate answers as needed.) c. Use the values in part (b) to determine...
Consider the following linear programming problem. Maximize p = 5x + 7y subject to the constraints 3x + 8y ≤ 1 4x - 5y ≤ 4 2x + 7y ≤ 6 x ≥ 0, y ≥ 0 Write the initial simplex tableau.
Ay 15 o o 12 An objective function and a system of linear Inequalities representing constraints are given Complete parts a through a Objective Function zu 4x - 2y Constraints 25x8 y22 x-12-2 6 -15 129 3 - 9 15 12 3 a. Graph the system of inequalities representing the constraints. Use the graphing tool to graph the system Click to enlarge graph Click the graph, choose a tool in the palette and follow the instructions to create your graph....
1. Solve the following linear programming problem by the method of corners. Maximize p=4x - 3y subject to x + 4y s 19 4x + ys 16 y20