A common method for determining the order quantity is called the single$-$period inventory model. This model fits your current situation because you are making only one single order for the holiday season. The maximum expected profit in the single$-$inventory model is based on the following formula:

where P$($Demand $<=$ Q$*)$ is the probability that demand is less than or equal to the recommended order quantity, Q$*.$ The term cu is the cost per unit of underestimating demand $($and losing sales because of going out of stock$)$ and co is the cost per unit of overestimating demand $($having unsold inventory$).$ So$,$

cu $=$ $$24-$ $$16=$ $$8$ lost per unit if Weather Teddy runs out of stock and

cu $=$ $$16-$ $$5=$ $$11$ lost per unit if left$-$over inventory must be sold at the clearance price.

Therefore

The graph titled Single$-$period Inventory Model for Weather Teddy shows a symmetrical normal distribution curve. Its peak corresponds to mu equal to $20000$ units. The vertical line divides the graph into two parts. The area under the curve and to the left of the vertical line is $0\mathrm{.}4211.$ The area under the curve and to the right of the vertical line is $0\mathrm{.}5789.$ To the left of the graph is written the following text: What quantity ordered $($Q$)$ corresponds to a probability of P equal to $0\mathrm{.}4211$ in order to maximize profit?

What is the optimal production $/$ order quantity in order to maximize profit?

a$.18,980$

b$.21,024$

c$.22,653$

d$.17,273$