Solve with excel

local semiconductor firm, Superchip, is planning its workforce and production levels over the next year. The firm makes a variety of microprocessors and uses sales dollars as its aggregate production measure, Based on orders received and sales forecasts provided by the marketing department, the estimate of dollar sales for the next year by month is as follows:

$\backslash$table$[[$Month$,\backslash$table$[[$Production$],[$Days$]],\backslash$table$[[$Predicted Demand$],[($in $$10,000)]]],[$January$,22,340],[$February$,16,380],[$March$,21,220],[$April$,19,100],[$May$,23,490],[$June$,20,625],[$July$,24,375],[$August$,12,310],[$September$,19,175],[$October$,22,145],[$November$,20,120],[$December$,16,165]]$

Inventory holding costs are based on a $25$ percent annual interest charge $($This means that $c_1=$ $$10,000**25\frac{\%}{12}=$$$208\mathrm{.}33$ per month$).$ It is anticipated that there will be $675$ workers on the payroll at the end of the current year and inventories will amount to $$120,000.$ The firm would

${?}^1$ From Nahmias and Olsen, Production and Openations Analytics $8^{th}$ edition $-$ section $3\mathrm{.}5$

like to have at least $$100,000$ of inventory at the end of December next year. It is estimated that each worker accounts for an average of $$60,000$ of production per year $($assume that one year consists of $250$ working days$).$ The cost of hiring a new worker is $$200,$ and the cost of laying off a worker is $$400.$

a$.$ Formulate as a linear program. Be sure to define all variables and include the required constraints

b$.$ Solve for the optimal solution. Round the variables in the resulting solution and determine the cost of the plan you obtain.