Assume that you own a small factory. A critical piece of machinery in your factory will need to be replacedin 180 days. If the machinery does not show up on time, you will need to shut down until it arrives. This might cause you to permanately lose customers.When you order the part you wil need to pay the $500,000 in advance. That is a lot of money for your small business. If you keep the money in the bank, it will earn interest each month. If you spend the money now, it will leave you with very litte money on hand, and you might have to borrow money to make payroll. You know from past experience that the delivery times are normally distributed with a mean of 45 days and a standard deviation of 15 days. When should you order the part? It is your company, but you must write up an explanation for your actions that convinces your investors that your actions are best. (Unfortunately, the investors cannot afford $500,000 at this time.) Explain why 135 days from now is the date to order it if you want to be 50% sure of getting the delivery on time.

Question

Assume that you own a small factory. A critical piece of machinery in your factory will need to be replacedin 180 days. If the machinery does not show up on time, you will need to shut down until it arrives.  This might cause you to permanately lose customers.When you order the part you wil need to pay the $500,000 in advance.  That is a lot of money for your small business. If you keep the money in the bank, it will earn interest each month.  If you spend the money now, it will leave you with very litte money on hand, and you might have to borrow money to make payroll. You know from past experience that the delivery times are normally distributed with a mean of  45  days and a standard deviation of  15 days.  When should you order the part?  It is your company, but you must write up an explanation for your actions that convinces your investors that your actions are best. (Unfortunately, the investors cannot afford $500,000 at this time.)  Explain why  135 days from now  is the date to order it if you want to be 50% sure of getting the delivery on time.