Question $3(11$ points$).$ ABC Co$.,$ a manufacturer of summer outdoor equipment, follows a make$-$to$-$order production policy. The fixed production cost is $9,000$ SAR for the manufacturer, and the variable production cost is $30$ SAR per unit. The retailer sells a unit for $100$ SAR in the season. If the products are not sold during the season, the retailer salvages them for $15$ SAR a piece. The wholesale price paid by the retailer to the manufacturer is $60$ SAR per unit. The retailer's demand is Normally distributed with a mean of $2,050$ units and a standard deviation of $500$ units. Use two decimal places in the calculations.

a$)$ What is the optimal order quantity of the retailer?

$"$b$)$ Find the optimal average profit of the retailer.

c$)$ Find the optimal average profit of the manufacturer.