1. Quarks sells three types of muesli, the Shoko, the Fruit & Nut, and the Berries Mix. Annual demands for the three products are DS = 50,000 for the Shoko, DF = 40,000 units for the Fruit & Nut, and DB = 30,000 units for the Berries Mix. Each type costs Quarks $2 per package. A fixed transportation cost of $1,000 is incurred each time an order is delivered. For each type ordered and delivered on the same truck, an additional fixed cost of $100 per type is incurred for receiving and storage. Quarks incurs an annual unit holding cost of 20 percent. Each product is ordered and delivered independently. a. What is the optimal order quantity for each product (round to the nearest integer)? (2pt) b. What is the optimal replenish cycle for each product (in weeks) (keep 3 decimals if needed)? Assume 52 weeks in a year. (2pt) c. What is the total annual cost including fixed ordering cost, variable ordering cost, and inventory holding cost for the company (keep 2 decimals if needed)? (2pt) Hint: Because each type is ordered and delivered independently, a separate truck delivers each type. Thus, a fixed ordering cost of $1,100 ($1,000 +$100) is incurred for each product delivery. 2. (Continued from question 2) The three product managers have decided to aggregate and order all three types each time they place an order. a. Evaluate the optimal order quantity (lot size) for each type (keep one decimal if needed). (3pt) b. What is the total annual cost including fixed ordering cost, variable ordering cost, and inventory holding cost for the company (keep 2 decimals if needed)? (2pt) c. Quantify using the total annual cost from Q1 c) and Q2 b) the impact of coordinated replenishment. Shall the managers coordinate their orders? (2pt) 3. (Continued from question 1) Suppose Quarks's Shoko supplier now offers quantity discount. If Quarks orders more than 20,000 (including 20,000) packages in a single order, it will be charged a discounted price for all units ordered. a. If the discount rate is 1%, find the optimal order quantity and total annual cost including fixed ordering cost, variable ordering cost, and inventory holding cost. (3pt) b. If the discount rate is 0.1%, find the optimal order quantity and total annual cost including fixed ordering cost, variable ordering cost, and inventory holding cost. (3pt)