A major equipment producer sells $4000$ units of its $$90/$unit product per year. Ordering costs are $$30$ and holding costs are $8\%$ of the product unit value per year. Each items requires $5$ square meters for storage $($product cannot be piled on top of each other$)$ and there is currently space in the warehouse. The space available is of size $20$ by $40$ meters to store the items.

a$)$ What lot size should he use?

b$)$ What should be the total stocking costs per year?

c$)$ Does he need additional space? How much, if any?