BZoom sells toy bricks2 that can be used to construct a wide range of machines, animals, buildings, and so on. It purchases a red dye powder to include in the resin it uses to make the bricks. The powder is purchased from a supplier for $1.30 per kg. At one production facility, UCZoom requires 800 kg of this red dye powder each week. BZooms annual holding cost rate is 30 percent and the fixed cost associated with each order to the supplier is $100 / order. Assume there are 7 working days per week, and 50 working weeks per year.

a. Determine the optimal amount of red dye powder BZoom should order from its supplier in each order, and the corresponding reorder interval (i.e., the time between orders) in days. Calculate the annual holding and setup cost incurred by your EOQ ordering policy.

b. Calculate a good reorder interval, the corresponding order quantity, and the annual holding and setup cost, if BZoom wants the reorder interval to be a power-of-two in days, e.g., 1, 2, 4, 8, 16, 32 days. Why is your reorder interval good? Why might a power-of-two reorder interval be used in practice?

c. Suppose BZoom can also buy blue dye powder from the same supplier (of red dye powder). BZoom requires 600 kg of the blue dye powder each week, the supplier charges $1.10 per kg of blue dye powder, and all other data are identical for red and blue dyes. For instance, BZoom still uses an annual inventory cost rate of 30% per year for each dye powder. If red and blue dyes are ordered separately, the fixed cost of each order to the supplier remains $100. However, if BZoom orders both blue and red dyes concurrently, the total fixed cost for this joint order is only $110 per order and not $100+100. Joint ordering saves on fixed order cost (due to shared resources such as transportation cost)! [Note: This can be a difficult question.]

c-1 Calculate a power-of-two reorder interval for the blue dye powder.

c-2 Would you advise BZoom to order red and blue dye powders independently using their respective EOQ or would you advise BZoom to coordinate orders for the two dye colors? Show annual cost calculations to support your recommendation (and the corresponding order quantities and reorder intervals you recommend).