Maximize z x 1 x 2 x 3 x 1 4 x 2 5 x 3 subject to 2 x 1 3 x...

Maximize: Z ( x 1 , x 2 , x 3 ) = x 1 + 4 x 2 + 5 x 3 , Subject to: 2 x 1 + 3 x 2 + x 3 <= 50 , 4 x 1 + 2 x 2 + 5 x 3 <= 40 , x 1 , x 2 , x 3 >= 0. Give the maximum value of Z , and do not include " Z = " in your answer.

Transcript

00:01 Hi, from the question given that, suppose that the given problem is maximize z is equal to 4x1 plus 10 x2 and the subject to the constraints are 2x1 plus x2 is less than are equal to 50 and 2x1 plus 5x2 which is less than are equal to 100 and 2x1 plus 3x2 which is less than are equal to 90 here the values or xi is greater than are equal to 0 we need to solve this problem by using the simplex method here all the constraints having less than are equal to type so we need to add the so we need to add the slack variables therefore maximize z can be written as 4 x1 plus 10 x2 plus 0 s 2 plus 0 s 2 plus 0 s2 plus 0 s 3 and the subject to the country are 2 x1 plus x2 plus slack variable s 1 which is equal to 50 and 2x1 plus 5x2 plus the slack variable s 2 which is equal to unread and 2x1 plus the slack variable s 2 and plus the slack variable s 2 and plus the slack variable s 2.

01:40 Which is equal to 90.

01:43 Now we move on to the iteration part.

01:46 So this is the iteration part.

01:48 Here cj is 410 0 0 that is the maximized z values and b is the slack variables s 1 s2 s3 and cb is 0 for the slack variable and xb is 50 and 90 and these are the coefficients of x1 x2 s2 s3.

02:07 Now, we need to find when z is equal to 0, zj is also equal to 0.

02:12 So here we need to find zj minus cj.

02:14 So 2 minus 4 is from this.

02:18 Sorry, 0 minus 4 is minus 4.

02:20 And 3, 0 minus 10 is minus 10.

02:25 0 minus 0 is 0 .0 is 0.

02:28 0 minus 0 is also 0.

02:29 Here we need to find the minimum value.

02:34 So here minus 10 is the minimum value.

02:37 So minimum value attains at the row x2 sorry column x2 therefore minimum ratio can be attained by dividing xb by the x2 so we have 1050 by 1 which is equal to 50 and red by 5 which is equal 20 and 90 by 3 which is equal to 30 so here also we need to find the minimum ratio so from this minimum ratio is 20 so the key element here is 5 so here we need to to enter the row as x2 and remove the slack variable s2 and make this row became one.

03:17 So we need to divide the r2 by 1 and then the remaining row became 0...

Question

Maximize: Z ( x 1 , x 2 , x 3 ) = x 1 + 4 x 2 + 5 x 3 , Subject to: 2 x 1 + 3 x 2 + x 3 <= 50 , 4 x 1 + 2 x 2 + 5 x 3 <= 40 , x 1 , x 2 , x 3 >= 0. Give the maximum value of Z , and do not include " Z = " in your answer.

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