Questions:

1. Write an IP model for this problem (comment on data, variables and constraints of the written model)

2. Formulate a model of the IP in PuLP using jupyter notebook (comment on data, variables and constraints of the formulated model)

A company produces industrial food for animals. This company has two types of product: powder and granules. The raw materials that is used for these two types of product are: oat, maize and molasses. The raw materials (with the exception of molasses) first need to be ground, and then all raw materials that will form a product are blended. In the last step of the production process the product mix is either transformed to granules or sieved to obtain food in the form of powder.

Every food product needs to fulfill certain nutritional requirements. The percentages of proteins, lipids and fibers contained in the raw materials and the required percentages in the final productsare listed in Table 1.

There are limits on the availability of raw materials. Table 2 displays the amount of raw material that is available every day and the respective prices.

The cost of the different production steps are given in the following table.

With a daily demand of nine tonnes of granules and twelve tons of powder, which quantities of raw materials are required and how should they be blended to minimize the total cost?

Figure 1: Animal food production process Table 1: Contents of nutritional components in percent Table 2: Raw material availabilities and prices Table 3: Production costs in /kg