Linear Programming Mixture Problem

[TheRedDevil18]

Homework Statement

Hi, I am having a problem with this particular type of problem. I am just so confused that I don't even know how to attempt these types of problems. Can someone please explain to me how to work with mixture problems.

 

[BruceW]

The first step is to think about the inequalities. This problem is really like any other linear programming problem, so don't get put off by the word 'mixture'. Think about what you have done in other linear programming problems.

 

[HallsofIvy]

Each fruit cake requires 500g of flour and 100g of sugar.
Each sponge cake requires 200g of flour and 200g of sugar.

So if she makes "x" fruit cakes she will need 500x grams of flour and 100x grams of sugar.
If she makes "y" sponge cakes she will need 200y grams of flour and 200y grams of sugar.

Putting those together, if she makes x fruit cakes and y sponge cakes she will need 500x+ 200y grams of flour and 100x+ 200y grams of sugar.

You are told that she has 2kg= 2000 grams of flour and 1.2 kg= 1200 grams of sugar. So what inequalities do you have? Switching the "<" to "=" will give you linear equations which can be graphed showing the boundaries of the regions where the inequalities are true.

 

[TheRedDevil18]

Each fruit cake requires 500g of flour and 100g of sugar.
Each sponge cake requires 200g of flour and 200g of sugar.

So if she makes "x" fruit cakes she will need 500x grams of flour and 100x grams of sugar.
If she makes "y" sponge cakes she will need 200y grams of flour and 200y grams of sugar.

Putting those together, if she makes x fruit cakes and y sponge cakes she will need 500x+ 200y grams of flour and 100x+ 200y grams of sugar.

You are told that she has 2kg= 2000 grams of flour and 1.2 kg= 1200 grams of sugar. So what inequalities do you have? Switching the "<" to "=" will give you linear equations which can be graphed showing the boundaries of the regions where the inequalities are true.

Okay, I think I understand what you are saying, you are basically grouping the ingredients together and comparing it to the minimum amount

x+y<=5
500x+200y<=2000
100x+200y<=1200

Are these correct?

 

[BruceW]

almost. rethink the 'direction' of the first inequality. She wants at least 5 cakes.

 

[TheRedDevil18]

almost. rethink the 'direction' of the first inequality. She wants at least 5 cakes.

Sorry, that should be x+y>=5

 

[BruceW]

yeah, looks good!