6.2.3 P = 30x, +x2(A) Using slack variables, determine the initial system for the linear programming problem.(B) Write the simplex tableau and identify the first pivot and the entering and exiting variables.(C) Use the simplex method to solve the problem.Maximizesubject to4x1 +X2 s 12X1 + 8x2 s 12Xq. X2 20(A) Using slack variables, determine the initial system for the linear programming problem. Use s, for the first constraint and s, for the second constraint.4x, +X2 +s1 = 12First constraintX1 + 8x2 + s2 = 12Second constraint– 30x, - x2 +P = 0Objective functionX1, X2, S1, S2 2(B) Write the simplex tableau by filling in the blanks below.X1X2S1S2411218112301The pivot element is located in the x, column and s, row.The enteringble is x,.The exiting variable is s,.(C) Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The maximum value is P = 90 when x, = 30 and x, =0.(Type integers or simplified fractions.)O B. There is no optimal solution.

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P= 30x, +x2 (A) Using slack variables, determine the initial system for the linear programming problem. (B) Write the simplex tableau and identify the first pivot and the entering and exiting variables. (C) Use the simplex method to solve the problem. Maximize 4x, +x2 s 12 X, + 8x2 s 12 X1. x, 20 subject to (A) Using slack variables, determine the initial system for the linear programming problem. Use s, for the first constraint and s2 for the second constraint. 4x, + X2 + S1 = 12 First constraint X1 + 8x2 + S2 = 12 - 30x, - x, +P = 0 Second constraint Objective function X1, X2, S1, S2 2 (B) Write the simplex tableau by filling in the blanks below. X1 X2 S1 S2 P 4 1 8 1 12 - 30 - 1 11 The pivot element is located in the x, column and s, row The entering variable is x,. The exiting variable is s,. (C) Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum value is P = 90 when x, = 30 and x2 = 0 (Type integers or simplified fractions.) O B. There is no optimal solution.