Consider the following LP problem. MAX: 9X1-8X2 Subject to: x1+x2≤6 -x1+x2≤3 3x1-6x2≤4 x1,x2≥0 Sketch the feasible...

Question

Question

Consider the following LP problem.

MAX: 9X₁-8X₂

Subject to: x₁+x₂≤6

-x₁+x₂≤3

3x₁-6x₂≤4

x₁,x₂≥0

Sketch the feasible region for this model.

What is the optimal solution?

What is the optimal solution if the objective function changes to Max.-9x1+8x2?

Answer 1

Answer #1

Replace inequality with equal sign in the constraints, solve the equations by giving one variable a hypothetical numerical value.
	x1	x2
x1+x2=6	-1	7
	6	0
-x1+x2=3	3	6
	-6	-3
3x1-6x2=4	-6	-2.3
	5.3	2
Please note that the 4th constraint of x1,x2>=0, gives us the Y axis as a constraint to consider.

00 -1,7 3,6 (4.4,1.6) Feasible Region (3,0) 15.3,2 (1.8,4.4) 16,0 0 (0,0) 61-6,-2.3 -6,-3

hence, the 4 options for x1 and x2 are:
x1	x2	9x1-8x2
4.4	1.6	26.8
1.8	4.4	-19
0	0	0
3	0	27

since the objective is to maximize the objective function, the maximum value is given by (4.4,1.6), hence, the value of x1=4.4, x2=1.6
Optimal solution
x1=	4.4
x2=	1.6

if the objective function is -9x1+8x2
x1	x2	9x1-8x2
4.4	1.6	-26.8
1.8	4.4	19
0	0	0
3	0	-27

since the objective is to maximize the objective function, the maximum value is given by (1.8,4.4),
Optimal solution
x1=	1.8
x2=	4.4

1 Replace inequality with equal sign in the constraints, solve the equations by giving one variable a hypothetical numerical

Answer 2

Similar Homework Help Questions

#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A,...

#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
Figure 1 provides the Excel Sensitivity output for the following LP model. 10x1 + 8x2 Max...

Figure 1 provides the Excel Sensitivity output for the following LP model. 10x1 + 8x2 Max Z= subject to: 31 +2x2 < 24 2x1 + 4x2 = 12 -2x1 + 2 x2 56 X1, X2 > 0 Variable Cells Cell Name $B$13 Solution x1 $C$13 Solution x2 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 6 0 10 1E+30 0 -12 8 12 1E+30 6 Constraints Cell $D$6 $D$7 $D$8 Name C1 Totals C2 Totals C3 Totals Final...
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this...

Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.

2. Solve the following LP problem graphically. Maximize profit = 3x1+ 5x2 Subject to:x2≤6 3x1 +...

2. Solve the following LP problem graphically. Maximize profit = 3x1+ 5x2 Subject to:x2≤6 3x1 + 2x2≤18 x1, x2≥0
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤...

Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0...

Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...

Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...

Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Consider the following linear programming model: Max X1 + X2 Subject to: X1 + X2 ≤...

Consider the following linear programming model: Max X1 + X2 Subject to: X1 + X2 ≤ 2 X1 ≥ 1 X2 ≥ 3 X1, X2 ≥ 0 This linear programming model has a(n). A. Unbound solution B. Infeasible solution C. Redundant constraint D. Alternate optimal solution
Solve the following LP problem graphically. Maximize profit = 3x1 + 5x2 Subject to: x2 ≤...

Solve the following LP problem graphically. Maximize profit = 3x1 + 5x2 Subject to: x2 ≤ 6 3x1 + 2x2 ≤ 18 x1, x2 ≥ 0

QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2...

QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2 20 How many extreme points exist in the feasible region for this problem? We cannot tell from the information that is provided The feasible e region is unbounded QUESTION 2 Given the following LP, answer questions 1-10 Minimize 2- 31+5x2 Subject to: 3x2x 24 2x1+4x2228 t is the optimal solution? (2, 6) (0, 12) (5,4.5) None of the...