A chef in a restaurant wants to design two types of salads. salad 1 and salad 2. There are 5 ingredients that could be included in any of them. lettuce, cucumbers. ham, nuts and goat cheese. each ingredient provides a certain amount of nutrients measured in nutrients per serving (npp) and represents a cost per serving that is included in the salad. This cost is different, depending on the salad in which it is included. The following table indicates the amounts of nutrients per serving included in the salad and the cost that one serving represents by type of salad.

Besides. the following requirements are met: salad 1 must contain at least two portions of lettuce, but no more than 4 of these portions must have at least two portions of walnuts and at most 3 portions of cucumber. Salad 2 must contain at least 3 pieces of lettuce, but no more than 5, at least three pieces of ham and at least two pieces of cucumber. The nutritional content of salad 1 must be at least 200 pp and that of salad 2 at least 550 pp. The total availability of ingredients to include in both salads is as follows, not all available portions may be used.

In addition, due to the cost of dairy, including goat cheese in salad 1 incurs a fixed cost of $8 regardless of the number of cheese servings included and a fixed cost of $10 if any are included. number of servings of cheese in salad 2. Servings of ingredients must be included in full in salads. Write a linear formulation that indicates the minimum cost to make the two salads. Clearly define the variables you use, also indicating the type of variable it is: integer, continuous or binary.

\begin{tabular}{lll} \hline & Number of \\ & Total \\ & Servings \\ & \multicolumn{2}{l}{ Available } \\ \hline Lettuce & & 14 \\ Cucumbers & & 22 \\ Ham & 57 \\ Walnuts & 43 \\ Goat Cheese & 55 \\ \hline \end{tabular}