In the final profit maximizing solution for the problem, which constraint(s) has(have) a slack/surplus variable(s) equal...
(A) Introduce slack, surplus, and artificial variables and form the modified problem, (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by applying the simplex method to the initial simplex tableau (D) Find the optimal solution of the original problem, fit exists Maximize P 4x1.5x2 subject to 2x1 + x2 28 X] + xy =21 X1, X220 ntents access access (A) Introduce slack, surplus,...
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...
please Question 1 Convert the constraints into linear equations by using slack variables. Maximize z = 2X1 +8X2 Subject to:X1 + 6x2 s 15 2x1 + 9x2 s 25 X120,X220 X1 + 6x2 +51 s 15 2X1 + 9x2525 25 x1 +6X2+S1 = 15 2X1 +9x2 +52 = 25 O X1 +6X2 + 512 15 2X1 + 9x2 +522 25 X1 +6x2 = S1 +15 2x1 + 9x2 = S2 + 25 Question 2 Introduce slack variables as necessary and...
1) What is the profit-per-unit at which the production plan will change for each type of wine? MAX Z = 9000X1 + 12000X2 ST 4X1 + 8X2 64 (Grapes) 5X1 + 5X2 50 (Storage) 15X1 + 8X2 120 (Processing Time) X1 7 (Demand for Valley Nectar Wine) X2 7 (Demand for Valley Red Wine) X1, X2 0 X1 X2 RHS Dual Maximize 9000 12000 Constraint 1 4 8 ...
Convert the following formulation to a 2 variable problem so that it can be solved graphically (HINT: Eliminate one of the variables – say X3...). Sketch the feasible region and compute the coordinates of its extreme points. 5X1 + X3 17 2X1 + 1.5X2 + X3 14 .5X1 + 2X2 + X3 10 X1 , X2 , X3 0 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm: Maximize profit: = $1x1 + $1x2 Subject to: $2x1 + $1x2 ≤ 100 $1x1 + $2x2 ≤ 100 a. What is the optimal solution to this problem? b. If a technical breakthrough occurred that raised the profit per unit of X1 to $3, would this affect the optimal solution? c. Instead of an increase in the profit coefficient X1 to $3, suppose that profit was overestimated...
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
Problem A: Consider the following LP problem to answer Questions 4 and 5. Maximise z = 5x1 + 4x2 Subject to 6X1 + 4x2 < 24 X1 + 2x2 5 6 -X1 + x2 <1 X2 < 2 X1, X2 > 0 Question 4 Refer to Problem A: Which of the following statements is correct? (1) The optimal value of x1 is in the interval [10, 15). (2) The optimal valu X2 is in the rval [0, 5). (3) The...
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual problem graphically. Identify the corner- point feasible (CPF) solutions and comer-point infeasible solutions for both problems. Calculate the objective function values for all these values. Identify the optimal solution for Z. I 피 University 2b. For each of the following linear programming models write down...