For the given maximization problem, (a) determine the number of slack variables needed, (b) name them, and (c) use Maximize z=5X1 +3X2 + X3 slack variables to convert each constraint into a linear equation. subject to: 8x1 + 9x2 + 10*3 s 166 4x1 + 8X2 + 13X3 5 227 with X1 20, X2 20, X3 20 a. How many slack variables are needed? b. Which slack variables should be used? OA. X1, X2 O B. $1, $2, 53 O C. X1, X2, X3 OD. S1, $2 c. What is the equation using a slack variable that corresponds to the first constraint, 8X, + 9%2 + 10%; $ 166? O A. 8X1 +9X2 + 10X3 + $1 = 166 O B. 8X1 + 9X2 + 10x3 + X1 = 166 O C. 8x1 + 9%2 + 10*3 5 166 O D. 8X1 + 9X2 + 10x3 + S, S 166 What is the equation using a slack variable that corresponds to the second constraint, 4x, + 8x2 + 13x3 $227? O A. 4X1 +8x2 + 13x3 5227 O B. 4X1 + 8x2 + 13x3 + $2 = 227 O C. 4X1 +8x2 + 13x3 +X2 = 227 O D. 4X1 +8x2 + 13x3 + $2 5227