Jim is a CFO of a mid-sized construction company. One of his key tasks is to ensure that the company has sufficient cash to pay its daily and hourly workers who are hired whenever need arises. The company operates all 365 days a year and Jim estimates that on any day his payroll is Normally distributed with mean $25,000 and standard deviation $7,000. Jim manages his cash reserves using the order-up-to model: each morning he places an order for cash with the bank and the armored vehicle arrives 2 days later with the money. It is company’s policy to pay all workers on the same day, but in rare cases when the company runs out of cash it pays workers as soon as possible while increasing their pay check by 1% for each day of delay. For each dollar carried the company incurs 15% cost annually which includes cost of capital and insurance.
What is the profit-maximizing order-up-to level for cash?