(EOQ) an automobile manufacturing plant uses exactly 8 power-lock mechanisms per hour. Each replenishment order to the supplier of the power-lock mechanisms incurs a fixed cost of $85. Each mechanism stored in inventory incurs a holding cost of $1.50 per week. a) Using the EOQ model, calculate the optimal order quantity, and the optimal average cost per year. b) suppose that the plant must order in power-of-two multiples of 1 week. (That is, the plant can place an order every week, or every 2 weeks, or every 4 weeks, … , or every 1/2 week, or or every 1/4 week,…) What is the optimal power-of-two order interval, and what is the cost ratio versus the optimal (non-power-of-two) solution?