Question Source My Open Math Math 125 Finite Math Section 43

Question Source: My Open Math (Math 125 Finite Math) Section 4.3: Linear Programming - The Simplex Method.

Consider the linear programming problem:

Maximize: P=60x+50y

{x+y80

{5x+10y560

{50x+20y1600

{x0

{y0

Use the simplex method to solve the problem. Use s, t, and u as your slack variables for the first, second, and third inequalities respectively. Use the final simplex tableau to identify the values below.

x =

y =

s =

t =

u =

P =

Solution

Use the simplex method to solve the problem:

x      y      s       t       u     p           
----------------------------------------------------
1      1      1      0      0      0      80   
5      10     0      1      0      0      560  
50     20     0      0      1      0      1600
-60    -50    0      0      0      1      0    

x      y      s       t       u     p           
----------------------------------------------------
0      0.6    1      0      -0.02 0      48   
0      8      0      1      -0.1   0      400  
1      0.4    0      0      0.02   0      32   
0      -26    0      0      1.2    1      1900

x      y      s       t       u     p           
-------------------------------------------------------
0      0      1      -0.075 -0.013 0      18   
0      1      0      0.13   -0.013 0      50   
1      0      0      -0.05 0.025 0      12   
0      0      0      3.3    0.88   1      3200

then answer is p = 3200; x = 12, y = 50