In Exercises 10-23 solve the indicated linear programming...

In Exercises 10-23 solve the indicated linear programming problem using the simplex method. 22. Maximize $z = -x_1 + 3x_2 + x_3$ subject to $-x_1 + 2x_2 - 7x_3 \le 6$ $x_1 + x_2 - 3x_3 \le 15$ $x_j \ge 0$, $j = 1, 2, 3.$

Transcript

00:01 High from the question given that maximum z is minus x1 plus 2 x2 plus x2 plus x 4 plus x5 minus 2 x 3 and subject to the constraints are minus x 1 plus x 2 x2 plus 2x 3 plus x 4 plus x 5 less than are equal to 12 and x1 this is not negative this is positive so x 1 plus 2 x2 plus x 3 plus x 3 plus x 3 plus x 5 plus 6 5 is less than are equal to 25.

00:34 Here all the x -is are greater than are equal to 0.

00:37 Now, here the constraints of the constraint 1 is of the type less than are equal to.

00:43 Therefore, we should add the slack variable.

00:45 So, when we introducing the slack variable, then the equation will be like this.

00:52 So now we are going to the iteration part.

00:55 So this is the i attrition part.

00:58 Here, cj.

00:59 C .j is nothing but a coefficient of the variable x1, x2, x3 s 1 s 2 s 3 in maximum z and b is the slack variables that we add s 1 s 2 s 3 here the slack variable c b is 0 0 0 and x b is the constant term that right that present in the right of the constraints so 12 18 24 and the x 1 x2 x 3 x 4 x 5 x 6 s 1 s 2 s 3 now here we need to mention the coefficient of all the variables now first let us assume that z is equal to 0 so z j is also be equal to 0 now we need to find z j minus c j so 0 minus 1 is negative 1 0 minus of minus 1 is positive 1 0 plus 2 is negative 2 0 minus 3 is minus 3 0 minus 1 is minus 1 0 minus 1 is minus 1 and 0 minus 2 is minus 2 is so we will get a zj minus cj like this here from z j minus z j minus z j minus z j we need to find the minimum value so minimum value is a obtained here for the column x3 so we need to find the minimum ratio by dividing xb divided by the x3 so we obtained 12 by 2 is 6 18 by 1 is 18 24 by 2 is 12 here we need to find the minimum ratio so minimum ratio is obtained here for the row s 1 so here the element 2 is the key element so here we need to entering the column x 3 in row and departing s 1 so here the key element is 2...

Question

In Exercises 10-23 solve the indicated linear programming problem using the simplex method. 22. Maximize $z = -x_1 + 3x_2 + x_3$ subject to $-x_1 + 2x_2 - 7x_3 \le 6$ $x_1 + x_2 - 3x_3 \le 15$ $x_j \ge 0$, $j = 1, 2, 3.$

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