Consider the nutritional $($diet$)$ planning problem discussed in the first lecture on LP applications. We will utilize the data of that model, but here we consider a $30-$day long time period for diet planning. Our objective is to find the minimum$-$cost breakfast menu that meets all stated nutritional requirements over the $30-$day time period. In other words, for example the calcium requirement is assumed to be met acceptably, if the total calcium intake over $30$ days meets the $30-$day requirement. $($Obviously$,$ this is a simplification: a more detailed dietary requirement over shorter times would be more realistic, but a bit more difficult to model.$)$ In order to make the nutritional plan more varied, we require that each breakfast choice listed in the data table $($titled Diet Planning Problem Data in the lecture$)$ appears on the $30-$day menu at least once. We also require that none of the breakfast choices appears more than seven times on the $30-$day menu. No partial breakfast choices are allowed, i$.$e$.,$ the number of each item selected for the $30-$day menu is a positive integer.

$1\mathrm{.}1.$ Formulate the optimization model of this problem. $(15$ points$)$

$1\mathrm{.}2.$ Implement and solve the problem using Excel. Develop your answer in an Excel worksheet tab called $$Diet$.$ Compare the cost of your solution to the one discussed in the lecture. $(15$ points$)$

$**$PLEASE DO NOT USE CHATGPT AS THIS DOES NOT PROVIDE THE RIGHT INFORMATION FOR THE PROBLEM. I WOULD LIKE TO SEE SCREESHOTS OF THE EXCEL WORKBOOK TO SEE WHAT FORMULAS AND EQUATIONS I SHOULD USE FOR THE MODEL$*$