A Company Needs to Hire Workers to Cover a 7

Essay

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 (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?