Problem 1 SECOND REQUEST ANSWER ONLY BONUS QUESTION. THIS WAS ANSWERED SEE BELOW. NEED BONUS QUESTION ANSWERED

Chapter 9: A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 65 pounds per week. The beans are purchased from a local supplier for $4 per pound. The coffeehouse estimates that it costs $50 in paperwork and labor to place an order for the coffee, and the annual holding cost is 20% of the purchasing price. (Use 52 weeks/year)

What is the economic order quantity (EOQ) for Colombian coffee?

What is the optimal number of orders per year?

What is the optimal interval (in weeks) between the orders?

(BONUS 5 points) Assume that the coffeehouses current order policy is to buy the beans every 13 weeks. The manager says that the ordering cost of S = $50 is only a guess. Therefore, he insists on using the current policy. Find the range of S for which the EOQ you found in part a) would be preferable (in terms of a lower total replenishment and carrying costs) to the current policy of buying beans every 13 weeks.

a. Economic Order Quantity is the optimal order size to minimize all inventory costs. The formula is written as

EOQ = [2FD/C]^1/2

Where C=Carrying cost per unit per year = In our problem the carrying cost is 20%of the purchasing price

which is 0.20(65 units*$4*52) = 2704

F=Fixed cost per order which is $50 for paperwork and others D=Demand in units per year is 65*52 =3380

Solving the above formula = ((2*50*3380)/2704)^(1/2) = (125)^(1/2) = 11.18

(b) Optimal number of orders per year

Optimal order quantity (Q*) is found when annual holding cost = ordering cost

solving for the above equation = Sqrt ((2*3380*50)/0.8) =650

holding cost per unit per year = 0.2*4 =0.8

What is the optimal interval (in weeks) between the orders?

T* = Q* /D = 650 /3380 = 0.1923 yrs

Assuming 52 weeks