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A Company Needs to Hire Workers to Cover a 7

Question 68

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A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are:
 Days af Week  Workers Requirad  Shift  Days off  Wage  Sunday 541 Sun & Man 900 Monday 502 Man & Tue 1000 Tuesday 363 Tue &Wed 1000 Wednesday 384 Wed&Thur 1000 Thursday 425 Thur & Fri 1000 Friday 406 Fri & Sat 900 Saturday 487 Sat & Sun 850\begin{array} { l c c l r } \text { Days af Week } & \text { Workers Requirad } & \text { Shift } & \text { Days off } & \text { Wage } \\\hline \text { Sunday } & 54 & 1 & \text { Sun \& Man } & 900 \\\text { Monday } & 50 & 2 & \text { Man \& Tue } & 1000 \\\text { Tuesday } & 36 & 3 & \text { Tue \&Wed } & 1000 \\\text { Wednesday } & 38 & 4 & \text { Wed\&Thur } & 1000 \\\text { Thursday } & 42 & 5 & \text { Thur \& Fri } & 1000 \\\text { Friday } & 40 & 6 & \text { Fri \& Sat } & 900 \\\text { Saturday } & 48 & 7 & \text { Sat \& Sun } & 850\end{array}  MIN: 900X1+1000X2+1000X3+1000X4+1000X5+900X6+850X7\text { MIN: } \quad 900 \mathrm{X}_{1}+1000 \mathrm{X}_{2}+1000 \mathrm{X}_{3}+1000 \mathrm{X}_{4}+1000 \mathrm{X}_{5}+900 \mathrm{X}_{6}+850 \mathrm{X}_{7}

 Subject to:\text { Subject to:}
X2+X3+X4+X5+X654X3+X4+X5+X6+X750X4+X5+X6+X7+X136X5+X6+X7+X1+X238X6+X7+X1+X2+X342X7+X1+X2+X3+X440X1+X2+X3+X4+X548Xi0 and integer \begin{array}{l}\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6} \geq 54 \\\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7} \geq 50 \\\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1} \geq 36 \\\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2} \geq 38 \\\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3} \geq 42 \\\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4} \geq 40 \\\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5} \geq 48 \\\mathrm{X}_{\mathrm{i}} \geq 0 \text { and integer }\end{array}

Based on this ILP formulation of the problem and the optimal solution (X1, X2, X3, X4, X5, X6) = (2, 10, 16, 6, 14, 8, 6) what values should go in cells B5:J13 of the following Excel spreadsheet?
 A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are:   \begin{array} { l c c l r }  \text { Days af Week } & \text { Workers Requirad } & \text { Shift } & \text { Days off } & \text { Wage } \\ \hline \text { Sunday } & 54 & 1 & \text { Sun \& Man } & 900 \\ \text { Monday } & 50 & 2 & \text { Man \& Tue } & 1000 \\ \text { Tuesday } & 36 & 3 & \text { Tue \&Wed } & 1000 \\ \text { Wednesday } & 38 & 4 & \text { Wed\&Thur } & 1000 \\ \text { Thursday } & 42 & 5 & \text { Thur \& Fri } & 1000 \\ \text { Friday } & 40 & 6 & \text { Fri \& Sat } & 900 \\ \text { Saturday } & 48 & 7 & \text { Sat \& Sun } & 850 \end{array}   \text { MIN: } \quad 900 \mathrm{X}_{1}+1000 \mathrm{X}_{2}+1000 \mathrm{X}_{3}+1000 \mathrm{X}_{4}+1000 \mathrm{X}_{5}+900 \mathrm{X}_{6}+850 \mathrm{X}_{7}    \text { Subject to:}    \begin{array}{l} \mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6} \geq 54 \\ \mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7} \geq 50 \\ \mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1} \geq 36 \\ \mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2} \geq 38 \\ \mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3} \geq 42 \\ \mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4} \geq 40 \\ \mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5} \geq 48 \\ \mathrm{X}_{\mathrm{i}} \geq 0 \text { and integer } \end{array}     Based on this ILP formulation of the problem and the optimal solution (X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, X<sub>4</sub>, X<sub>5</sub>, X<sub>6</sub>) = (2, 10, 16, 6, 14, 8, 6) what values should go in cells B5:J13 of the following Excel spreadsheet?

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