An inventory manager for a furniture manufacturing company has collected the necessary information to determine the optimal production policy for a Louis V bed model. The marketing department has ensured him/her that the demand for this model over the next year will be constant at a rate of 20 units per month. The production manager is maintaining a constant production rate of 45 units per month. He/She has also estimated a setup cost of $1000 per production run and a unit manufacturing cost of $300. The finance department advised the inventory manager to use a monthly interest rate of 10%.

1- Find the optimal production policy.

2- The inventory manager decided to allow shortages at a monthly cost of $1/3 per unit. What is the new production lot size, maximum shortages level, and monthly total system cost?