A fruit juice company makes two special drinks by blending apple and pineapple j

Question

A fruit juice company makes two special drinks by blending apple and pineapple juices. The profit per liter is $0.60 for the first drink and $0.50 for the second. the portions of apple and pineapple juice in each drink are shown in the table.

Ingredient            First Drink               Second Drink

Apple juice              30%                         60%

Pineapple Juice       70%                         40%

There are 1000 liters of apple juice and 1500 liters of pineapple juice available. Use the simplex method to find the number of liters of each drink that should be produced in order to maximize the profit.

Explanation / Answer

Maximize profit p = 0.6x+0.5y

subject to .3x+.6y <= 1000,

.7x+.4y <= 1500

x,y >=0

Tableau #1
x y s1 s2 p   
0.3 0.6 1 0 0 1000   
0.7 0.4 0 1 0 1500   
-0.6 -0.5 0 0 1 0

Tableau #2
x y s1 s2 p   
0 0.428571 1 -0.428571 0 357.143   
1 0.571429 0 1.42857 0 2142.86   
0 -0.157143 0 0.857143 1 1285.71   

Tableau #3
x y s1 s2 p   
0 1 2.33333 -1 0 833.333
1 0 -1.33333 2 0 1666.67
0 0 0.366667 0.7 1 1416.67

x = 1666.67 litres, y = 833.333 litres

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