Consider the following linear program (LP):

max z= 2x1 + x2 3x3 +5x4

s.t. x1 +2x2 +3x3 +4x4 40

2x1 x2+ x3+2x4 8

4x12x2+ x3 x4 10

x1, x2, x3, x4 0

1. Use the simplex method to solve this model; details in doing so are stated below.

(a) Convert the LP model to an equation form by adding the necessary slack or surplus variables.

(b) Identify basic and nonbasic variables, state their corresponding values, and create the first simplex tableau.

(c) State why optimality is not attained yet.

(d) Identify basic and nonbasic variables and state their corresponding values.

(e) What is the pivot column? State why.

(f) What is the pivot row? State why.

(g) What is the pivot element for this first simplex tableau?

(h) What is the entering variable?

(i) What is the exiting variable?

(j) Create the second tableau.

(k) Show your work how you got the new pivot row in this second tableau.

(l) Show your work how you got your new z-row in this second tableau.

(m) If optimality is not attained, carry on with new simplex tableaux until it is done. Provide all your

sub-sequent tableaux. You do not need to show your work in how you got these tableaux.

(n) What is the optimal z and the optimal point (x1, x2, x3, x4)?