Linear Programing

PROBLEM 5

Let  X1 = number of lbs of phosphate to be used in the mixture

        X2 = number of lbs of potassium to be used in the mixture

Objective function:

            Minimize Cost (C) = P50X1 + P60X2

Subject to:

            X1 + X2 = 100

                     X1 < 30

                     X2 > 15

                     X1 > 0

                     X2 > 0

The complete set of constraints can now be expressed as follows:

            X1 + X2 + A1 = 100

                     X1 +  S1 =  30

            X2 – S2  + A2  = 15

                               X1 > 0

                               X2 > 0

                                S1 > 0

                                A1 > 0

                                A2 > 0

            C = 50X1 + 60X2 + OS1 = 100A1 + 100A2

|Cj |  |  |50 |60 |0 |0 |100 |100 |

|z |2 |3 |0 |0 |0 |0 |0 | |

|s1 |3 |2 |1 |0 |0 |0 |24 | |

|s2 |1 |2 |0 |1 |0 |0 |12 | |

|s3 |0 |1 |0 |0 |1 |0 |4 | |

|s4 |1 |0 |0 |0 |0 |1 |8 | |

At each iteration of the Simplex algorithm, we want to enter a new variable to the basis and remove an old variable from the basis so that the value of z improves (decreases) and the feasibility of all feasible variables is maintained.

The entering variable is determined by examining the reduced costs of the non-basic variables. The reduced cost of a variable represents the...