Question

Average Inventory The DeMarco Pasta Company receives 600 cases of imported San Marzano tomato sauce every 30 days. The number of cases of sauce on inventory t days after the shipment arrives is

N(t)=600-20√30t
Find the average daily inventory.

Answer 1

Answer: The average daily inventory is 200 cases.

Explanation:

Since we have given that

N(t)=600-20√30t

We need to find the average daily inventory.

`(1)/(b-a)\int\limits^a_b {600-20√(30t)} \, dt\\\\=(1)/(30)\int\limits^(30)_0 {600-20√(30t)} \, dt \\\\=(1)/(30)[600t-(20(30t)^(3)/(2))/(45)|_0^(30)\\\\=(1)/(30)[18000-(20* 30^3)/(45)]\\\\=(1)/(30)[18000-12000]\\\\=200`

Hence, the average daily inventory is 200 cases.