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
Consider the following linear programming model: Max X1 + X2 Subject to: X1 + X2 ≤...
Consider the following linear programming model Max 2X1 + 3X2 Subject to: X1 + X2 X1 ≥ 2 X1, X2 ≥ 0 This linear programming model has: A. Infeasible solution B. Unique solution C. Unbounded Solution D. Alternate optimal solution E. Redundant constraints
Consider the following linear programming problem. Maximize 5X1 + 3X2 Subject to: X1 + X2 ≤ 20 X1 ≥ 5 X2 ≤ 10 X1, X2 ≥ 0 What are the optimal values of X1 and X2 respectively?
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?
Problem 1: Consider the following linear optimization problem: max 1 +22x;3 subject to x1 + x2 +r3 10 2x1 -r2 2-4 i20, -1,2,3 a) Bring the problem to a standard form (b) Show that the point (2,8,0)T is optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set 1) (d) Find...
You are given the following linear programming model in algebraic form, with X1 and X2 as the decision variables: Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts). Minimize 40X1+50X2 Subject to 2X1+3X2>=30 2 X1+ X2>=20 X1>=0, X2>=0 a) Graph the feasible region and label the corner point. Compute the optimal solution using any method of your choice. Justify your answer and indicate the optimal solution on your graph....
Solve the following Integer Linear Programming Problem graphically using the method presented in class. Indicate whether problem is unbounded, infeasible and if an optimal solution exists, clearly state what the solution is. MAX Z = X1 + 2X2ST 4X1 + 6X2 ≤ 22 X1 + 5X2 ≤ 15 2X1 + X2 ≤ 9 X1, X2 ≥ 0 and X1 integer
Problem 1: Consider the following linear optimization problem: max +22 +rs subject to X1 + X2 + X3 = 10 2x1 - 22 24 i 20, 1,2,3. (a) Bring the problem to a standard form. (b) Show that the point (2,8,0)Ts optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers. (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set...
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)...
5. Suppose that (x1, X2, X3) is a feasible solution to the linear programming problem 4r, +2x2 + x3 minimize X12 3, 2a 23 2 4, subject to Let y and ybe non-negative numbers (a) Show that x1(y2y2)2(-y12) + x3y2 2 3y14y2 1 (b) Find constraints on yi and y2 so that 4x12 2 x1(y1 + 2¥2) + x2(-y1 + Y2) + x3Y2 1 at every feasible solution (xi, x2, X3) (c) Use parts (a) and (b) to find a...
2. Consider the following linear model where c has not yet been defined. Max z = C1x1 + x2 s.t. X1 + X2 <6 X1 + 2.5x2 < 10 X1 2 0,X220 Use the graphical approach that we covered to find the optimal solution, x*=(x,x) for all values of - Sci so Hint: First draw the feasible region and notice that there are only a few corner points that can be the optimal solution. Also remember that if the objective...