11) Maximize z» x 1 + 2x2 subject to: x1+ x2 s20 3x1+ 2x2 40 2x13x2 60 x1z0 x20 Use th perfor x1 ...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks) Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Question 12 Convert the constraints into linear equations by using slack variables. Maximize z = X1 + 2x2 + 3x3 Subject to: X1 + 9x2 + 3x3 = 40 6X1 + X2 + 6x3 s 50 X120,X220, X320 O X1 + 9x2 + 3x3 = 51 +40 6x1 + x2 +6x3 = S2 + 50 O X1 +9x2 + 3x3 +51 = 40 6x1 + x2 + 6x3 +S2 = 50 X1 +9x2 + 3x3 +51 = 40 6X1 +...
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...
Question 19 Find the pivot in the tableau. X1 X2 X3 X4 X5 X6 Z 2 3 6 1 0 0 0 10 2 1 2 0 0 0 20 4 04 0 0 1 040 -2 4 -8 0 1 0 یہ نہ مانم plonu 1 oloor 1 in row 2, column 5 6 in row 1, column 3 O 3 in row 1, column 2 4 in row 3, column 1 Question 16 5 p Write the expression...
(1) Convert the following LPs to standard form: 22 (a) max z 3x1 + 2x2 s.t. 21 < 40 X1 + x2 < 80 2x1 + x2 < 100 X1, X2 > 0 (b) max z = 2x1 s.t. X1 – X2 <1 2x1 + x2 > 6 X1, X2 > 0 (c) max z = 3x1 + x2 s.t. 1 > 3 X1 + x2 < 4 2x1 – X2 = 3 X1, X2 > 0
Consider the simplex tableau given below. X1 X2 S1 S2 Р 1 4 2 3 - 3 0 1 0 0 3 24 0 -6 0 1 0 (A) The pivot element is located in column and row (B) The entering variable is (C) The exiting variable is O. (D) Enter the values after one pivot operation in the tableau below. X1 X2 S1 S2 Р 1 2 0 3 0 -4 1 1 0 12 09 96 0 1...
Question 9 Find the value(s) of the function on the given feasible region. Find the maximum and minimum of z = 8x + 8y. K0,5) (5/2,5) (0,4) (6,0) (10,0) 56,32 80,32 -32,-56 48,40 Question 11 Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. In V10192 In 10+ 3 Int+2 in v 01/ in In 90t + 2 in v Jin In 10+ 3 Int + In v In 10 +...
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54 x1 + x2 = 3 and X120, X2 0. DI (a) Solve this problem graphically. (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. I (c) Continue from part (b) to work through the simplex method step...
Consider random variables X and Y with the joint pdf fx1,x2(x1,x2) = 3x1, 0 < x2 < x1 <1. Calculate P(X2 < 1/2 | X1 >= 3/4)
Given the LPP: Max z=-2x1+x2-x3 St: x1+x2+x3<=6 -x1+2x2<=4 x1,x2<=0 What is the new optimal, if any, when the a) RHS is replaced by [3 4] b) Column a2 is changed from[1 2] to [2 5] c) Column a1 is changed from[1 -1] to [0 -1] d) First constraint is changed to x2-x3<=6 ? e) New activity x6>=0 having c6=1 and a6=[-1 2] is introduced ?