# Operations Research 03I: Linear Programming Blending Problem

In this video, I’ll talk about how to formulate

a special type of LP problem called the blending problem. In a blending problem, various inputs are

blended in some desired proportion to produce the final goods. This type of problems are commonly seen in

real-world applications. For example, blending various types of crude

oils to produce different types of gasoline and other outputs. Blending various types of metal alloys to

produce various types of steels. Mixing different types of food ingredients

to provide required proportions of nutrients. Let’s see an example. An agricultural mill produces animal feed

mix by combining limestone, corn, and soybeans. Interesting facts: milled limestone in animal

feed will provide calcium for bone development and help the formation of egg shells. Here are the nutrition facts: 1kg of limestone

contains 0.38kg of Calcium, 0kg or Protein, and 0kg of Fiber. For 1kg of Corn, these values are 0.001, 0.09,

and 0.02. For 1kg of Soybeans, these values are 0.002,

0.5, and 0.08. Each kg of the final product must contain

at least 0.008kg but no more than 0.012kg of Calcium, at least 0.22kg of Protein, and

at most 0.05kg of Fiber. The prices of each kg of limestone, corn,

and soybeans are $0.1, $0.2, and $0.4, respectively. We want to find the feed mix that meet all

these requirements with minimum cost. To simplify this problem, we assume that we

only make 1kg of feed mix. We define three decision variables: L is the

kg of limestone needed, C is the kg of corn needed, and S is the kg of soybeans needed

in the feed mix. We want to minimize the total cost, which

is equal to the unit cost of limestone times its quantity, plus the unit cost of corn times

its quantity, plus the unit cost of soybeans times its quantity. The feed mix is made of only limestone, corn,

and soybeans. So, these components should add up to 1kg. The feed mix must contain a certain amount

of the nutrients. The amount of Calcium is bounded by 0.008

and 0.012. The amount of Protein should be at least 0.22

but should not exceed 1. The amount of Fiber should be at most 0.05,

but it will never be less than 0. The amount of each component should be nonnegative

and each should not exceed 1, which is the total. This is the complete problem formulation. Okay, that’s how to formulate the blending

problem. Thanks for watching.

you didn't demonstrate how to solve it…..

I have a question on a blending LP problem. Would I be able to ask you about it and you could let me know if I’m on the right track

this video gets zero point zero zero Likes.

This is not blending though. This is just a regular LP model.

Hi Guys, please comment and let me know what you think about this Operations Research Open Course. Your feedback is really appreciated. If you enjoy the video, please subscribe and share. All my replies here are only related to the content in my own videos. I am afraid I won't be able to answer other questions. Thanks for your understanding.