Example Problem No. 2 (1 of 3)Solve the following modelgraphically:Maximize Z = 4x₁ + 5x₂subject to: x₁ + 2x₂ ≤ 106x₁ + 6x₂ ≤ 36x₁ ≤ 4X1, X₂ ≥ 0Step 1: Plot the constraintsas equationsX₂10864202The feasible region is above the line 6x1+6x2=36.The feasible region is below the line 6x1+6x2=36.The feasible region is to the right of x1=4.|x₁ = 4- 6x₁ + 6x₂ = 36X₁ + 2x₂ = 104 6 8 10 X₁Figure 2.23 Constraint Equations2-46

Answered: Example Problem No. 2 (1 of 3) Solve…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Similar questions

QUESTION 15 Calculate the minimum value of 3x + 6y subject to the following constraints: x+y22 x + 2y ≤ 5 x+y≤6 x ≥ 0 y≥0
Complete the following. Maximize f = 2x + 4y subject to 5x + 4y 0 , γ > 0. (a) State the given problem in a form from which the simplex matrix can be formed (that is, as a maximization problem with < constraints). f = < 36 < -2 х, у 20 (b) Form the simplex matrix. y S1 S2 first constraint second constraint objective function Determine the first pivot entry. The first pivot is in row column
QUESTION 14 Calculate the maximum value of 4x + 6y subject to the constraints below: 3x + y ≤ 16 x + 3y ≤ 16 y≥ 1 x ≥ 0
In the problem, find the miimum value of z = 4x + 5y, subject to the following constraints: 2x+y≤6; x≥0; y ≥0; x+y≤5 (1,-4) is a vertex of the feasible region. True or False
Find the maximum for the linear programming problem:
1) Find the values of x1 and x2 that maximize f(x1, x2) = 5 + In(x1) + In(x2) such that 2x,? + x,? < 3, x1 2 0, and x2 2 0. 2) If we add more constraints to the above problem, how will that affect the optimal value of the objective? That is, will the maximum value of the objective become larger, smaller, or unchanged if extra constraints are added to the above problem?
Consider the following maximization problem. Maximize subject to the constraints 5x1 I1 201 P = 10x₁ + x₂ - 5x3 x₁ ≥ 0 I₂ +9x3 90 15x2 + 3x3 0 T3 > 0 82 Introduce slack variables and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. P X3 81 I1 X2 83 RHS
2. Graph the ff: in one cartesian plane and find the feasible region(select darkest color for region of the set of solutions) Constraints: 4 x-3y ≤ 1 3x+2y2l ysl x20 } 3. Referring to problem no. 2, find the minimum and maximum values of the objective function: Z=2x-y
Find the maximum value of z = 3x1 + 2x2 + 4x3 Objective function subject to the constraints 3x1 + 2x2 + 5x3< 18 4x1 + 2x2 + 3x3< 16 2x1 + x2 + x32 4 Constraints where x1 2 0, x, z 0, and x3 0.
Given the following linear problem Minimize z = 5x1 + 2x2 + 6x3, subject to: 4X1 + 2x₂ + x3 ≥ 12 3x1 + 2x2 + 3x3 ≤18 X1 + 3x₂ + 4x3 ≤ 13 x ≥ 0, y ≥ 0 a.) Rewrite the problem as a standard maximum problem by modifying constraints as necessary. Clearly identify your final problem. b.) Set up the initial simplex tableau. c.) Your initial solution may be infeasible. Circle a possible pivot element in the tableau for Phase I of the simplex method. Explain your choice, but you do not need to perform the pivot.
6. Consider a constrained optimisation problem with the objective function f(x) = 3x + 2y and the constraint 2x+y=10. Find the maximum value of f(x) within the feasible region.

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS