Suppose the annual demand is normally distributed with mean $50,000$ units and standard deviation of $1,000$ units. The company receives an average profit margin of $$20$ per unit. To account for loss of goodwill, let$$s assume that a lost sale has a penalty cost of $$10.$ What is the optimal capacity that a manufacturing company should have for this product if a marginal unit of capacity costs $$10?$ Assume that the capacity is going to be used for ever.

Group of answer choices

$50,670$

$50,440$

$49,560$

$50,840$