Retailer Staffing problem. The campus store has decided to hire some students to work part time helping customers and performing various functions that used to be contracted out to outside vendors. There are two work shifts per day (AM and PM) and the store is open five days a week. Exactly one student must be assigned to each shift. To become sufficiently familiar with the stores operations, each student that is hired must work at least two shifts per week. The store has identified a pool of eight qualified students from which to hire. For each student, the store has estimated how much he or she would add to the stores profit, per shift worked. This information is shown in the table below. The table also marks each shift for which a particular student is available with a 1. Finally, it also gives the maximum number of shifts per week that each student can work. To maximize its profits, which students should the store hire and which shifts should each student work?

Check your answer and layout: CM, GR, JE and SR work and maximum profit is 910.

use this spreadsheet and show formulas

also show solver screenshot

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow[t]{2}{*}{ Student } & \multirow{2}{*}{\begin{tabular}{l} Profit \\ /Shift \\ (\$) \end{tabular}} & \multicolumn{2}{|c|}{ Mon } & \multicolumn{2}{|c|}{ Tue } & \multicolumn{2}{|c|}{ Wed } & \multicolumn{2}{|c|}{ Thu } & \multicolumn{2}{|l|}{ Fri } & \multirow[t]{2}{*}{ Max shifts } \\ \hline & & AM & PM & AM & PM & AM & PM & AM & PM & AM & PM & \\ \hline CM & 100 & 1 & & & & 1 & 1 & 1 & & & & 3 \\ \hline FI & 50 & & 1 & & 1 & & 1 & & 1 & & 1 & 4 \\ \hline GR & 95 & & 1 & 1 & & & 1 & & 1 & 1 & & 2 \\ \hline HS & 75 & & & 1 & & & & 1 & & 1 & 1 & 2 \\ \hline JD & 70 & & & & & 1 & & & & 1 & & 2 \\ \hline JE & 90 & & & & & & & 1 & 1 & 1 & & 2 \\ \hline SR & 80 & 1 & & & 1 & 1 & & & 1 & 1 & 1 & 3 \\ \hline TR & 85 & & 1 & & & & 1 & & & & 1 & 2 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{14} & A & B & C & D & E & F & G & H & 1 & J & K & L & M & N & 0 & p & Q \\ \hline & & & & & & & & & & & & & & & & & \\ \hline \multicolumn{18}{|l|}{2} \\ \hline 3 & & Student & \begin{tabular}{l} Profit/Shift \\ (\$) \end{tabular} & \multicolumn{2}{|c|}{ Mon } & \multicolumn{2}{|c|}{ Tues } & \multicolumn{2}{|c|}{ Wed } & \multicolumn{2}{|c|}{ Thurs } & \multicolumn{2}{|c|}{ Fri } & & Max Shifts & Min Shift & \\ \hline 4 & & & & AM & PM & AM & PM & AM & PM & AM & PM & AM & PM & & & & \\ \hline 5 & & CM & 100 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & & & & \\ \hline 6 & & FI & 50 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & & & & \\ \hline 7 & & GR & 95 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & & & & \\ \hline 8 & & HS & 75 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & & & & \\ \hline 9 & & JD & 70 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & & & & \\ \hline 10 & & JE & 90 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & & & & \\ \hline 11 & & SR & 80 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & & & & \\ \hline 12 & & TR & 85 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & & & & \\ \hline 13 & & & & & & & & & & & & & & work or not & Workot*Max Shifts & Total shifts worked & Workot * Min Shifts \\ \hline 14 & Hire & CM & & & & & & & & & & & & & & & \\ \hline 15 & for & FI & & & & & & & & & & & & & & & \\ \hline 16 & shift & GR & & & & & & & & & & & & & & & \\ \hline 17 & or not & HS & & & & & & & & & & & & & & & \\ \hline 18 & & JD & & & & & & & & & & & & & & & \\ \hline 19 & & JE & & & & & & & & & & & & & & & \\ \hline 20 & & SR & & & & & & & & & & & & & & & \\ \hline 21 & & TR & & & & & & & & & & & & & & & \\ \hline 22 & & & shift & & & & & & & & & & & & & profit & \\ \hline 23 & & & covered & equal & equal & equal & equal & equal & equal & equal & equal & equal & equal & & & & \\ \hline 24 & & & Ones & & & & & & & & & & & & & & \\ \hline \end{tabular}