Gilbert's business has taken off and he's trying to create a production plan. His beginning inventory in January is $500$ units. His demand is forecast to be $600$ units in January, $800$ in February, $1200$ in March, $1700$ in April and $300$ in May. Presuming $20$ working days per month, $8$ hours per day per worker and a production of $2$ units per day per worker, if he has two workers and no overtime, will he end up May with a backorder, an overstock or no inventory or backorder?

a$.$ backorder

b$.$ neither backorder or inventory

c$.$ inventory