Please help me with these Math Problems thank you! Maximize the function z = x +

Question

Please help me with these Math Problems thank you!

Maximize the function z = x + 3y subject to the constraints: 3x + 7y lessthanorequalto 21, 3x + 2y lessthanorequalto 12, x greaterthanorequalto 0, y greaterthanorequalto 0. Maximize the function z = x + y + 2w subject to the constraints: x + 2y + w lessthanorequalto 4, 3x + y + w lessthanorequalto 3, x greaterthanorequalto 0, y greaterthanorequalto 0, w greaterthanorequalto 0. Be sure to display the initial tableau, as well as any successive tableaus. At the end, list the values of all variables, including the slack variables. Check to see that those values agree with the objective function and the constraints.

Explanation / Answer

Solution:

(1.)

Using simplex method

for given contraint and function z

Tableau #1
x y s1 s2 z Result   
3 7 1 0 0 21   
2 1 0 1 0 12   
-1 -3 0 0 1 0

Tableau #2
x y s1 s2 z Result

0.428571 1 0.142857 0 0 3   
1.57143 0 -0.142857 1 0 9   
0.285714 0 0.428571 0 1 9   

therefore from abve table

Optimal Solution where function is maixmize z = 9; at x = 0, and y = 3

(2)

Using again simplex method for given constraints and function z

Tableau #1
x y w s1 s2 z   
1 2 1 1 0 0 4
3 1 1 0 1 0 3
-1 -1 -2 0 0 1 0

Tableau #2
x y w s1 s2 z
-2 1 0 1 -1 0 1
3 1 1 0 1 0 3
5 1 0 0 2 1 6

from above

Optimal Solution where maximize z = 6 at x = 0, y = 0, w = 3

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