System design and operation

1. How is quantity determined in inventory control? Cover EOQ (including quantity discounts and EPQ), FOI, and the Single Period Model. In addition, give simple examples with input information, tabulation, graphs, and calculations of each of the following making up your own data. Explain as you proceed. (80 points)a. EOQ with quantity discounts using a constant holding costb. EPQc. FOId. Single Period Model with discrete measures using the Poisson distribution2. Discuss when inventory is replenished. Give a simple example of an ROP with variable demand with constant lead time. Make up your own data. Explain as you proceed. (20 points)