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.
[tex]\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[/tex]
Hence, the average daily inventory is 200 cases.
