A hog raiser is mixing two types of grains, A and B.

- Each unit of grain A costs P50 and contains 20 grams of fat and 10 grams of protein.
- Each unit of grain B costs P80 and contains 30 grams of fat and 30 grams of protein.

The hog raiser wants each unit of the final product to yield at least 180 grams of fat and at least 120 grams of protein.

How many units of each type of grain should he use to meet these requirements?

This problem is an example of linear programming. We create equations and constraints based on the provided data, then graph them to find the feasible region that minimizes cost. It might need additional tools or software to solve.

Explanation:

This is a problem of linear programming, a mathematical approach used for optimising an objective function given a series of constraints. To solve this problem, we need to create equations based on the given information in the question. First, we can start with the cost. The cost function will be 50A + 80B, where A and B represent the units of grains type A and type B respectively.

For the protein, the constraint is 10A + 30B >= 120, since we need at least 120 grams of protein. For the fat, the constraint is 20A + 30B >= 180 because we need at least 180 grams of fat.

The hog raiser's goal is to minimize the cost under the above constraints. Graphing these inequalities, identifying the feasible region and finding the vertex points will help us determine the minimum cost.

This is a complex problem and might require the help of software to solve. However, understanding the formulation is a good first step in linear programming problems.

Learn more about Linear Programming here:

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