You are working for Dire Wolf Industries $($DWI$),$ helping them run their Sales & Operations Planning $($S&OP$)$ program for a line of make to stock items. Specifically, you are running the aggregate planning model to help assist the Chief Operating Officer $($COO$)$ and the Vice President of Sales to agree upon the next $12$ months plan.

The aggregate model is attached here. The model provided here is offered without any input data. That data is provided below, and you must enter it by hand into the spreadsheet. When solving this model, while the number of workers must be an integer, the amounts of money, hours and items do not have to be integers. The solver settings can be seen here.

Part $1$

$0\mathrm{.}0/2\mathrm{.}0$ points $($graded$)$

The model provided above is offered without any of the input data. The demand data for the model is provided below, and you must enter it into the spreadsheet. The aggregate monthly demand of the item is as follows:

January February March April

$110681001290766932$

May June July August

$4036209211722932$

September October November December

$51086044794812268$

The remaining data for the model is provided below, and you must enter it into the spreadsheet. Please enter the input values with all the decimal values given below.

Material cost $($$$/$unit$)$: $16\mathrm{.}7875$

Inventory holding costs $($$$/$unit$/$month$)$: $3\mathrm{.}6125$

Cost of stockouts $($$$/$unit$/$month$)$: $6\mathrm{.}5875$

Cost for hiring and training new worker: $2125\mathrm{.}0$

Cost for laying off an employee: $4250\mathrm{.}0$

Labor hours required per item produced: $0\mathrm{.}84$

Regular worker cost $($$$/$month$)$: $2040\mathrm{.}0$

Overtime cost $($$$/$hour$)$: $14\mathrm{.}4196$

Outsourcing cost $($$$/$item$)$: $38\mathrm{.}4625$

Hours worked by employee per month: $175\mathrm{.}84$

Max overtime $($hours$/$month$/$employee$)$: $12\mathrm{.}32$

Starting inventory: $2000\mathrm{.}0$

Ending inventory $($min$)$: $2000\mathrm{.}0$

Starting backlog: $0\mathrm{.}0$

Allowable ending backlog $($max$)$: $0\mathrm{.}0$

Starting workforce: $24\mathrm{.}0$

Ending workforce $($min$)$: $24\mathrm{.}0$

Ending workforce $($max$)$: $24\mathrm{.}0$

Base price $($$$/$item$)$: $44\mathrm{.}8375$

You want to develop an initial aggregate plan for the next $12$ months. Use the initial data provided above and assume that there are no planned promotions or discounts over the next $12$ months. Find the optimal plan over the next $12$ months. Based on this optimal solution, answer the following questions.