Question: A store has an inventory of Q units of a product at time t = 0. The store sells the product at the steady rate of Q/A units per week, and it exhausts the inventory in A weeks.
(a) Find a formula f(t) for the amount of product in inventory at time t. Graph f(t).
(b) Find the average inventory level during the period 0 ≤ t ≤ A. Explain why your answer is reasonable.