# Blue Rock Candy Empire

### By Nate Ewbank, October 4th, 2013

### Blue Rock Candy Linear Programming

For this project, I will be planning out how to maximize my profits for selling my blue rock candy.

### My Business

My business here would be selling blue rock candy. The stuff is very simple to make, you heat up sugar, cornstarch and water, add some color and flavoring, let cool, and then BOOM!, you've got your candy. I've decided to sell it in two different quantities, a small bag (containing approximately 15kg of blue rock candy) and a large bag (containing approximately 125 kg of blue rock candy).

### The Costs

Making the blue rock candy in those large quantities won't just be a stroll in the park. It's gonna cost something. I don't want to waste the $10K I've been given, so I'm going to limit spending to $6000. To make one small bag (15 kg), it would cost me about $15. For making a large bag (125 kg) it would cost me about $45. So to set this up in an equation, we can find this out with 15x+45y≤6000.

### Selling My Product

So with selling my product, we should have to try and make a profit. What i want to do is sell no more than 200 bags. To set this up as an equation, I'm taking the measurement of kilograms of one bag plus the other. So this should look like 15x+125y≤200.

### Step Four: Profit!

Finally we have to set up a profit equation. So, to get profit, we must subtract our cost from our sell. So setting it up would be P= (15x+125y)-(15x+45y), and when we solve this, we get P= 80y.

### Restrictions

The restrictions that will go with the selling of my product will be as follows: x ≥ 0, y≥0, and then we have our equations, 15x+45y≤6000, and 15x+125y≤200.

### The Graph

### Maximizing Profit

Looking at the graph, it is kind of hard to see how we can maximize our profit. But on the bright side, our profit equation is quite hefty as well, being as it is P= 80y. Looking at the graph, the largest sum of y we got was (0, 1.6). So in order to maximize our profit, we must sell 128 of the large bags.