Use the simplex method to solve the linear programming problem. Maximize z = 7x_
ID: 3406530 • Letter: U
Question
Use the simplex method to solve the linear programming problem. Maximize z = 7x_1 + 2x_2 + x_3 subject to: x_1 + 4x_2 +5x_3 lessthanorequalto 119 x_1 + 4x_2 + 10x_3 lessthanorequalto 238 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 = 119. B. There is no maximum solution to this linear programming problem.Explanation / Answer
solve
x1 x2 x3 s1 s2 s3 s4 s5 z
----------------------------------------------------------------------------
1 4 5 1 0 0 0 0 0 120
1 4 10 0 1 0 0 0 0 240
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
-7 -2 -1 0 0 0 0 0 1 0
x1 x2 x3 s1 s2 s3 s4 s5 z
----------------------------------------------------------------------------
1 4 5 1 0 0 0 0 0 120
1 4 10 0 1 0 0 0 0 240
-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
-7 -2 -1 0 0 0 0 0 1 0
x1 x2 x3 s1 s2 s3 s4 s5 z
----------------------------------------------------------------------------
1 4 5 1 0 0 0 0 0 120
1 4 10 0 1 0 0 0 0 240
-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
-7 -2 -1 0 0 0 0 0 1 0
x1 x2 x3 s1 s2 s3 s4 s5 z
----------------------------------------------------------------------------
1 4 5 1 0 0 0 0 0 120
1 4 10 0 1 0 0 0 0 240
-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
-7 -2 -1 0 0 0 0 0 1 0
x1 x2 x3 s1 s2 s3 s4 s5 z
----------------------------------------------------------------------------
1 4 5 1 0 0 0 0 0 120
0 0 5 -1 1 0 0 0 0 120
0 4 5 1 0 1 0 0 0 120
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
0 26 34 7 0 0 0 0 1 830
Answer is:
z = 830; x1 = 120, x2 = 0, x3 = 0
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