$($a$)$ Identify the problem in the college diet case plan using the available information$($b$)$ What are the key assumptions in this case?$($c$)$ Formulate as an LP problem, define the decision variables, objective function and constraints.$($d$)$ Find the optimal solution. $($e$)$ What is the cost per meal?$($f$)$ Is this a well$-$balanced diet?$($g$)$ Include the details of your analysis $($using QM for Windows or Excel QM$)$ as an appendix to your report. Do not include any output in the body of the report.