XYZ Company is preparing its aggregate production plan for $2022.$ The monthly demand forecasts are given in Table $1.$Table $1$Monthly Demand ForecastsMonthDemand$15002600360048005130062000725008300092400101800111500121200$The company is expected to have $100$ workers on the payroll and $150$ units in inventory at the end of $2021.$ Each worker can produce $10$ units per month on regular time and $2$ units per month in overtime.Additional data:$1.$Regular time production cost$-$$$200$ per unit$\mathrm{.}2.$Overtime production cost$-$$$300$ per unit$\mathrm{.}3.$Hiring cost$-$$$500$ per worker$4.$Firing cost$-$$$3000$ per worker$5.$Desired final inventory $($December $2022)-100$ units$6.$Desired final workforce $($December $2022)-150$ workers$7.$Inventory holding cost is charged based on the average inventory at the beginning and endof the month at $$50$ per unit per month$8.$No shortages areallowed.a$.$Determine a production plan using the $$chase strategy$.$b$.$Determine a production plan using the $$level strategy$.$c$.$Formulate a LP model that will determine the optimal production plan for $2022.$You must define your variables clearly, write out the constraints that must be satisfied explaining the significance of each, and write the objective function with explanation.d$.$Solve the LP model usingExcel Solver. You should also submit your Excel file.e$.$Compare the three production plans $($chase strategy, level strategy, and LP solution$)$ with respect to the following:i$.$Monthly inventory levelsii.Hiring and firingiii.Overtime useiv.Total cost