Answer to Question #181901 in Operations Research for Peter

Question

b) The Farmer decides to buy his bags of food A and food B from another store. This store sells a bag of food A for $9 and a bag of food B for $11. However, the farmer realised the new food bags are perishable. If the farmer does not use an entire bag, the food will spoil. The farmer must now use all of the contents of each bag. Use the linear programming process for this scenario to determine how many bags of food A and B the farmer now needs to meet the animals' minimum daily requirements for a minimum cost. Does the Farmer save any money but purchasing from another store?

Answer 1

In store 1: Type A price =6 , total bags=12, while Type B price =8 and total bags =16 

In store 2: Type A price =9 , total bags=x while Type B price =11 and total bags=y

Forming inequality :

x + y < (12 +16) ......................1

9x+11y < ((12*6)+(8*16)) .......................2

Therefore, 

x + y < 28

9x + 11y < 200

Eliminating x,

9x + 9y < (28*9)

9x + 11y < 200

_____________________________

    -2y = -52

_____________________________

Therefore ,

y=26

Replacing y in the equation

x + 26 < 28

x=2

In store 2 Type A bags =2  and Type B bags =26

The farmer does not save money since 252 > 200