Johns dog, Barry, every day eats on average 2 pounds of kibble with a standard deviation of 0.25 pounds. John buys the kibble from an online retailer that charges $2 per pound of kibble. The retailer has a delivery fee of $10 per order, regardless of how much dog food is ordered and consistently delivers in 2 days. Living in a small house John does not have too much storage space, so he estimates that keeping a pound of kibble in the cabinet essentially costs him $0.1 per week. Barry the dog, or course, does not pay for food. The retailer has two different sizes for kibble: 60-pound bags and 90-pound bags. If he runs out, he needs to replace the missing kibble with an equal amount of wet food which costs more, at $6 per pound. Note that Z.0.75 = 0.67, Z.0.67 = 0.43, Z.0.33 = -.43 and there are 365 days per year.

a) (7 points) Ethan needs to know when to place an order for kibble. At what level is the kibble (in pounds) when Ethan needs to place an order? How much safety stock should Ethan target? ANSWER: ROP = 4.15 lbs SS = 0.15 pounds

b) (5 points)If Ethan orders the 60-pound bags, what are his annual inventory costs? ANSWER: $278.46/yr

c) (5 points) If Ethan orders the 90-pound bags, what are his annual inventory costs? ANSWER: $315.51/yr

d) (1 point) Which size should Ethan order every time he places an order? Explain. ANSWER: 60 lbs (plus explanation)

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