A consulting firm is trying to determine how to minimize the annual costs associated with the purchase of paper. Each time an order is placed, a cost of $ 20 is incurred. The price per paper box depends on the number q, the number of boxes ordered (according to the table shown below). The annual retention cost is 20% of the inventory value in dollars. During each month, the consulting company uses 80 paper boxes. Determine the optimal order quantity, the number of orders each year and the total annual cost.
Number of ordered Boxes | Price per box |
q < 300 | $10.00 |
300 ≤ q < 500 | $9.80 |
q ≥ 500 | $9.70 |