Question: Consider the following LP problem: maximize earnings= $0.80X1 + $0.40X2 + $1.20X3 - $0.10X4 subject to:

X1 + 2X2 + X3 + 5X4 Less than or equal to 150

X2 – 4X3 + 8X4 = 70

6X1 + 7X2 + 2X3 – X4 Greater than or equal to 120

X1, X2, X3, X4 Greater than or equal to zero

a) Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problem’s objective function.

b) Set up the complete initial simplex tableau for this problem. Do not attempt to solve.

c) Give the values for all variables in this initial solution.