Natalia manages the inventory of organic whole wheat flour at an

Natalia manages the inventory of organic whole wheat flour at an...

Natalia manages the inventory of organic whole wheat flour at an organic store in Plano, TX, which is sold in bags of 50 pounds. The demand for flour is 12 bags a day. The flour is purchased from a local farm which charges $12 per bag. Exactly one day after Natalia places an order for bags of flour to the farm, her (otherwise unemployed) brother Yash comes back from the farm with the ordered quantity. Sending her brother to pick up the order costs Natalia $40 per trip. Storing a bag of flour for one week (7 days) costs $3 in storage costs. The cost of capital for the store is currently equal to 10% per week. The key parameters for the EOQ model are:

D = 12 bags per day = 84 bags per week.

P = $12.

I = 10%.

K = $40. 

h = 3 + 10% × 12 = $4.2 per bag per week (= $0.6 per bag per day). 

A) How much should Natalia order every time she places an order to the farm in order to minimize her total cost per week (in numbers of bags)?

B) Suppose Natalia's brother refuses to go to the farm more than once a week.  How much should Natalia order every time she places an order to the farm in order to minimize her total cost per week? Carefully explain.