A firm has $56$ units of product X on hand. Forecasts of demand are for $20$ units per week. A production quantity of $100$ units is planned for period $3.$ Customer orders are $24$ for period $1,18$ for period $2,$ and $15$ for period $3.$

What is the projected on hand inventory at the end of period $2?$

Multiple Choice

$14$

$32$

$12$

$20$

$22$