$3$ a$)$ A company uses $1,250$ large cans of tomatoes a month, at an average rate of $50$ per

day for each of the $25$ days per month the company is working. Usage can be approximated by a normal distribution with a standard deviation of $3$ cans per day. Lead time is constant at $5$ days. Monthly carrying costs are $1$ per can and ordering costs are $100$ per order.

i$.$ Determine the economic order quantity.

ii$.$ Find the variable inventory costs per month.

iii. For a service level of $98$ per cent, how many cans of tomatoes should the company have on hand when it places the order?