A lawnmower manufacturer has a demand forecast for the next $12$ months as shown in the table below. The current workforce of $100$ staff can produce $1,500$ lawnmowers per month. Lawnmowers must be stored at ground level and need space of $2$ metres x $1\mathrm{.}5$ metres each.

$($a$)$ Prepare a production plan that keeps the output level and fully utilises the workforce. What is the maximum warehouse space required under this plan? Lawnmower Demand Forecast

Month $/$ Demand Forecast $($mowers$/$month$)$

January $600/$ February $800/$ March $-1,000/$ April $-1,500/$ May $-2,000/$ June $-1,700/$

July $-1,200/$ August $-1,100/$ September $900/$ October $-2,500/$ November $3,200/$ December $-900$