Solution:
First we have to find the roots of each equation by applying x1=0 & x2=0.
Consider x1 + x2 =6 as equation1 and x1 + 2.5x2 =10 as equation 2.
In the below attachement, we can find the roots of the equation.
Therefore the optimum solution is max z = 6c1; for all the values of -∞ ≤c1≤∞ Since x1 = 6, x2 = 0
2. Consider the following linear model where C1 has not yet been defined. Max s.t. z...
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...
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...
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...
alim Universitesi LMS adi Consider the following linear programming model Maximize z = 3x1 + 2 X2 s.t. Xi 54 X1 + 3x2 = 15 2X1 + X2S TO X 30 X220. Calculate the value of the objective function for each of the corner-point (extreme point) solutions. Use this information to identify the optimal solution. Fill the table below with your answers. Extreme-point (x1.x2) Objective Value feasible Z solutions
Solve the following linear programming problems as directed. Put in a box the values of all the variables you use in your solution, as well as the optimal value of the objective function. a) SIMPLEX METHOD Max Z = 11X1 + 10X2 s.t. 2 X1 + X2 <= 150 4 X1 + 3 X2 <= 200 X1 + 6 X2 <= 175 X1, X2 >= 0 b) GRAPHIC METHOD (do not forget to indicate the feasible region) Min Z = 30...
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 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 program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y ≥ 10 1X + 3Y ≥ 90 X, Y ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Conduct a sensitivity analysis to determine the range of optimality for the objective function coefficients X & Y. c. What are the binding constraints? d. If the right-hand-side of the binding constraints are marginally increased, what will be the Dual Value?
Problem 2-10 (Algorithmic) For the linear program Max 3 A + 3 B s.t. A + 3B ≤ 9 10A + 6B ≤ 30 A, B ≥ 0 select the correct graph that identifies the optimal solution. What is the value of the objective function at the optimal solution? (i) BA (ii) BA (iii) BA (iv) BA The value of the objective function at the optimal solution is .
Answers please Production and Operations Management (29:623:311) Spring 2019 3. A linear programming model is given as follows: maximize Z = 50x1 + 80x2 + 64x3 + 80x4 Subject to 5xit 2.5x2 +4.5x3 +3.99x, S 600 4.1x, + 2.6xz +5.5x +1.9x, S 500 15x, 22x2 +18x3 +25x4 S 400 8x+ 12.6x2 +9.7x3 +10.55x4 S 1700 x1 + x2 2 0.60 (a) Solve the problem by using excel solver. (b) What are the sensitivity ranges for the objective function coefficients? (c)...