Question: One of the formulas for inventory management says that the average weekly cost of ordering, paying for, and holding merchandise is

Where q is the quantity you order, k is the cost of placing the order (the same, no matter how often you order), c is the cost of one item (a constant), m is the number of items sold each week (a constant), and h is the weekly holding cost per item (a constant),

(a) Find the quantity that will minimize A(q).

(b) Shipping costs sometimes depend on order size. When they do, it is more realistic to replace k with k+bq, the sum of k and a constant multiple of q. What is the most economic quantity to order now?

Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

A. Explain the problem in your own words.

B. What mathematical concepts learned in this module apply to this problem?

C. Explain the steps you must take to solve this problem.

D. What is the most difficult aspect of solving this problem?

E. Explain exactly what the answer means from a mathematical perspective.