Show all your work $($typed in the document or pasting a scanned image of your handwritten solution$).$ Save your solution document in a $.$pdf file and upload it to Canvas along with an Excel file for calculations performed in Excel.

Problem $1(30$ points$)$

BestArtRepro, Ltd$.,$ produces a variety of art replicas. Prepare an aggregate plan for the next six months using the following information.

$\backslash$begin$\{$tabular$\}\{$lrccccc$|\}$

$\backslash$hline & $\backslash$multicolumn$\{7\}\{$c$\}\{$ MONTH $\}\backslash \backslash$

& $1$ & $2$ & $3$ & $4$ & $5$ & $6\backslash \backslash$

$\backslash$hline Demand & $160$ & $150$ & $160$ & $180$ & $170$ & $140\backslash \backslash$

Capacity & & & & & & $\backslash \backslash$

Regular & $150$ & $150$ & $150$ & $150$ & $160$ & $160\backslash \backslash$

Overtime & $10$ & $10$ & $0$ & $10$ & $10$ & $10\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Cost Per Unit$\}\backslash \backslash$

$\backslash$hline Regular time & $\backslash$$$50\backslash \backslash$

$\backslash$hline Overtime & $75\backslash \backslash$

$\backslash$hline Subcontract & $80\backslash \backslash$

$\backslash$hline Invertory holding. per month & $4\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Subcontracting can handle a maximum of $10$ units per month. Beginning inventory is zero. Develop a plan that minimizes total cost. No back orders are allowed. Regular capacity $=$ Regular production. $($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

Use the table template below to provide your answer, or to reproduce it in Excel.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & & & & & & & & $\backslash \backslash$

$\backslash$hline & & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $\backslash \backslash$

$\backslash$hline Demand & & & & & & & & $\backslash \backslash$

$\backslash$hline Capacity & & & & & & & & $\backslash \backslash$

$\backslash$hline & Regular & & & & & & & $\backslash \backslash$

$\backslash$hline & Overtime & & & & & & & $\backslash \backslash$

$\backslash$hline & & & & & & & & $\backslash \backslash$

$\backslash$hline & & & & & & & & $\backslash \backslash$

$\backslash$hline Production & & & & & & & & $\backslash \backslash$

$\backslash$hline & Regular & & & & & & & $\backslash \backslash$

$\backslash$hline & Overtime & & & & & & & $\backslash \backslash$

$\backslash$hline & Subcontrat & & & & & & & $\backslash \backslash$

$\backslash$hline Inventory & & & & & & & & $\backslash \backslash$

$\backslash$hline & average inventory & & & & & & & $\backslash \backslash$

$\backslash$hline & & & & & & & & $\backslash \backslash$

$\backslash$hline & & & & & & & & $\backslash \backslash$

$\backslash$hline Cost & & & & & & & & $\backslash \backslash$

$\backslash$hline $\backslash$$$50$ & Regular & & & & & & & $50\backslash \backslash$

$\backslash$hline $\backslash$$$75$ & Overtime & & & & & & & $\backslash$$$0\backslash \backslash$

$\backslash$hline $\backslash$$$80$ & Subcontrat & & & & & & & $\backslash$$$0\backslash \backslash$

$\backslash$hline $\backslash$$$4$ & Ave Inventory & & & & & & & $\backslash$$$0\backslash \backslash$

$\backslash$hline & & $\backslash$$$0$ & $\backslash$$$0$ & $\backslash$$$0$ & $\backslash$$$0$ & $\backslash$$$0$ & $\backslash$$$0$ & $0/0\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$