Problem $3(22$ points$)$

The food bank annual fund$-$raising drive is scheduled to take place next week. Donations are collected during the day and night by e$-$transfer, and through in$-$person contact. The average donation resulting from each type of contact is as follows.

$\backslash$table$[[,$E$-$transfer $($$$),$In Person $($$$)],[$Day$,20,40],[$Night$,30,75]]$

The food bank has enough donated gasoline and cars to make at most $300$ in$-$person contacts during one day and night. The volunteer minutes required to conduct each type of contact are as follows.

$\backslash$table$[[,$E$-$transfer $($min$),$In$-$Person $($min$)],[$Day$,5,12],[$Night$,4,10]]$

The charity has $25$ volunteer hours available each day and $35$ volunteer hours available each night. The chairperson of the fund$-$raising drive wants to know how many different types of contacts to schedule in a $24-$hour period $($i$.$e$.,$ one day and one night$)$ to maximize total donations.

$($a$)$ Formulate algebraically a Linear Programming model for this problem $(12$ points$).$

Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel Solver $($Provide the corresponding "Excel Spreadsheet" and the "Answer Report"$).$ Include "managerial statements" that communicate the results of the analyses. $($i$.$e$.,$ describe verbally$/$narratively the results. $(10$ points$)$