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.

Step-by-step explanation:

Since we have given that

N(t)=600-20√30t

We need to find the average daily inventory.

$\dfrac{1}{b-a}\int\limits^a_b {600-20\sqrt{30t}} \, dt\\\\=\dfrac{1}{30}\int\limits^{30}_0 {600-20\sqrt{30t}} \, dt \\\\=\dfrac{1}{30}[600t-\dfrac{20(30t)^\frac{3}{2}}{45}|_0^{30}\\\\=\dfrac{1}{30}[18000-\dfrac{20\times 30^3}{45}]\\\\=\dfrac{1}{30}[18000-12000]\\\\=200$

Hence, the average daily inventory is 200 cases.