Question

Maximizar P=2x+3y+5z

Sujeto a: x+2y+3z ≤ 12

               x-3y+2z ≤ 10

                x ≥ 0, y ≥ 0, z ≥ 0

Maximize P=2x+3y+5z

Subject to:

x+2y+3z ≤ 12

x-3y+2z ≤ 10

                x ≥ 0, y ≥ 0, z ≥ 0

Answer 1

Simplex Method is used.

Calculate Δj value as a difference of Cj-Zj row and it is termed as Net Evaluation Row (NER).

A simplex table indicates the current solution to be optimum when all the values in the Δj row are either

• negative or zero when linear programming is for maximization or
• positive or zero when linear programming is for minimization.

The current problem is for maximization. so, we select the highest positive value in the Δj row and the selected column is called key column. with the variable in the column head as incoming variable. Now divide the bi values from the corresponding element of key column to get Replecement ratio column. in this column we always select the minimum positive value irrespective of weather the problem is for maximization or for minimization. the selected row is called Key row and the variable in the row is termed as outgoing variable. the element at the intersection of Key column and key row is called key element. Key element is converted to unity and this is dine by multiplying or dividing a common multiplying factor. Now, all the element in the key column are made zero except key element which will be unity. this is done by adding or subtracting the proper multiple of key row from other row. in the new table outgoing variable is replaced by incoming variable.