Consider the following LP problem:

Maximize earnings = $0.80X1 + $0.40X2 + $1.20X3 - $0.10X4

Subject to X1 + 2X2 + X3 + 5X4 150 X2 - 4X3 + 8X4 = 70 6X1 + 7X2 + 2X3 - X4 120 X1, X2, X3, X4 0

a. Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problems objective function. (20%) b. Set up the complete initial simplex tableau for this problem. Do not attempt to solve. (20%)) c. Give the values for all variables in this initial solution. (10%))