Use the simplex method to solve the linear programming problem. Maximize z = 10x
ID: 3032472 • Letter: U
Question
Use the simplex method to solve the linear programming problem. Maximize z = 10x_1 + 2x_2 + x_3 subject to: x_1 + 4x_2 + 9x_3 lessthanorequalto 115 x_1 + 4x_2 + 10x_3 lessthanorequalto 249 with x_1 greaterthanorequalto 0, x_2 greaterthanorequalto 0, x_3 greaterthanorequalto 0. Select the correct choice below and. if necessary, fill in the answer box to complete your choice. A. The maximum is when x_1 =, x_2 =, x_3 =, s_1 = 0, and s_2 = 134. B. There is no maximum solution to this linear programming problem.Explanation / Answer
x1 +4x2 + 9x3 <=115
x1 +4x2 +10x3 <= 249
x1>=0 ; x2>=0 ; x3>=0
z = 10x1 + 2x2 +x3
Tableau #1
x1 x2 x3 s1 s2 s3 s4 s5 p
1 4 9 1 0 0 0 0 0 115
1 4 10 0 1 0 0 0 0 249
1 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-10 -2 -1 0 0 0 0 0 1 0
Tableau #2
x1 x2 x3 s1 s2 s3 s4 s5 p
1 4 9 1 0 0 0 0 0 115
1 4 10 0 1 0 0 0 0 249
-1 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-10 -2 -1 0 0 0 0 0 1 0
Tableau #3
x1 x2 x3 s1 s2 s3 s4 s5 p
1 4 9 1 0 0 0 0 0 115
1 4 10 0 1 0 0 0 0 249
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-10 -2 -1 0 0 0 0 0 1 0
Tableau #4
x1 y1 x3 s1 s2 s3 s4 s5 p
1 4 9 1 0 0 0 0 0 115
1 4 10 0 1 0 0 0 0 249
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
-10 -2 -1 0 0 0 0 0 1 0
Tableau #5
x1 x2 x3 s1 s2 s3 s4 s5 p
1 4 9 1 0 0 0 0 0 115
0 0 1 -1 1 0 0 0 0 134
0 4 9 1 0 1 0 0 0 115
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
0 38 89 10 0 0 0 0 1 1150
Optimal solution : p = 1150; x1 = 115, x2 = 0, x3 = 0
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