Bonus Problem: $(6$ points$)($Bonus points will be added to your homework score$).$

A fish distributor is trying to perfect his business to maximize the money he saves. Daily fish sales are normally distributed with a mean of $575$ pounds and a standard deviation of $75$ pounds. The distributor sells each pound of fish for $$4\mathrm{.}60$ and pays $$1\mathrm{.}40$ per pound to buy fish. The distributor must get rid of unsold fish by paying a waste removal facility fee of $$0\mathrm{.}40$ per pound of fish. How many pounds of fish should the distributor order each day and what $\%$ of the time will he experience a stock$-$out? Are there any drawbacks to the order size proposed and how could the fisherman address such issues?

Bonus Problem: $(6$ points$)($Bonus points will be added to your homework score$).$

A fish distributor is trying to perfect his business to maximize the money he saves. Daily fish sales are normally distributed with a mean of $575$ pounds and a standard deviation of $75$ pounds. The distributor sells each pound of fish for $$4\mathrm{.}60$ and pays $$1\mathrm{.}40$ per pound to buy fish. The distributor must get rid of unsold fish by paying a waste removal facility fee of $$0\mathrm{.}40$ per pound of fish. How many pounds of fish should the distributor order each day and what $\%$ of the time will he experience a stock$-$out? Are there any drawbacks to the order size proposed and how could the fisherman address such issues?