Ms$.$ Burke also provided the following data and estimates for the next year: unit production cost $=$$$70\mathrm{.}00$; inventory$-$holding cost $=$$$140$ per unit per month; lost sales cost $=$$$200$ per unit; overtime cost $=$$$6\mathrm{.}50$ per unit; undertime cost $=$$$3\mathrm{.}00$ per unit; and production$-$rate$-$change cost $=$$$5\mathrm{.}00$ per unit, which applies to any increase or decrease in the production rate from the previous month. Initially, $900$ units are expected to be in inventory at the beginning of January, and the production rate for the past December was $9,100$ units. She believes that monthly demand will not change substantially from last year, so the mower unit sales figures for the last year in the Performance Lawn Equipment Database should be used for the monthly demand forecasts.

Your task is to design a spreadsheet that provides detailed information on monthly production, inventory, lost sales, and the different cost categories and solve a linear optimization model for minimizing the total cost of meeting demand over the next year. Compare your solution with the level production strategy of producing $9,100$ units each month. Interpret the Sensitivity Report and conduct an appropriate study of how the solution will be affected by changing the assumption of the lost sales costs. Summarize all your results in a report to Ms$.$ Burke.