Question $1(10$ points$)$

Using excel solver

A manufacturer provides specialized microchips. During the next $3$ months, its sales, costs, and available time are

$\backslash$begin$\{$tabular$\}\{$lccc$\}$

$\backslash$hline & Month $1$ & Month $2$ & Month $3\backslash \backslash$

$\backslash$hline Chips required at the end of the month & $1000$ & $2500$ & $2300\backslash \backslash$

Cost $-$ regular time $(\backslash$$$/$chip$)$ & $105$ & $110$ & $113\backslash \backslash$

Cost $-$ over time $(\backslash$$$/$chip$)$ & $110$ & $120$ & $125\backslash \backslash$

Storage cost $(\backslash$$$/$chip$/$month$)$ & $10$ & $5$ & $5\backslash \backslash$

Regular operation time $($hr$/$month$)$ & $2625$ & $2625$ & $2625\backslash \backslash$

Maximum Overtime operation $($hr$/$month$)$ & $480$ & $480$ & $480\backslash \backslash$

$\backslash$hline

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

There are no chips in stock at the beginning of the first month. It takes $1\mathrm{.}5$ hr of production to produce a chip.

The cost to store a chip starts from the beginning of one month to the next $($i$.$e$.,$ if a chip is produced in month $1,$ regardless the date of the month, storage fee will be charged from beginning of month $1).$

Determine a production schedule and the total cost that meets the demand requirements, does not exceed the monthly production time limitations$,$ and minimizes cost.

Note that no chips should be in stock at the end of the $3$ months.