Q: You are creating a batch of protein bars and want your product to have as much protein in it as possible using two food sources A & B. Source A provides 5g of protein per pound and source B provides 4g of protein per pound. In a batch of the protein bar you do not want more than 4 pounds in total weight. Source A costs $2/pound and B $1/pound. You also want to keep the price of the entire batch to be lesser than $5.

Practical Optimization

A: This is a good example of an application for the simplex algorithm. The simplex algorithm works quite well for problems that can be formulated in a linear manner with linear constraints. For example, if we assume the optimal amount of source A is \(x\) pounds and source B is \(y\) pounds, the objective function we want to maximize (the protein in the bars) can be formulated as follows

$$

\text{Protein} = 5x + 4y\\

$$

subject to constraints

$$

x + y \le4\\

2x + y\le 5\\

$$

The optimal solution can be found using the simplex algorithm. The alg…

Practical Optimization

A: This is a good example of an application for the simplex algorithm. The simplex algorithm works quite well for problems that can be formulated in a linear manner with linear constraints. For example, if we assume the optimal amount of source A is \(x\) pounds and source B is \(y\) pounds, the objective function we want to maximize (the protein in the bars) can be formulated as follows

$$

\text{Protein} = 5x + 4y\\

$$

subject to constraints

$$

x + y \le4\\

2x + y\le 5\\

$$

The optimal solution can be found using the simplex algorithm. The alg…