Question

Evaluate lim x→0 e x − x − 1 cos x − 1 . 2. A warehouse selling cement has to decide how often and in what quantities to reorder. It is cheaper, on average, to place large orders, because this reduces the ordering cost per unit. On the other hand, larger orders mean higher storage costs. the warehouse always reorders cement in the same quantity, q. The total weekly cost, C, or ordering and storage is given by C = a q + bq, where a and b are positive constants. (a) Which of the terms a/q and bq represents the ordering cost and which represents the storage cost? (b) What value of q gives the minimum total cost?

Answer 1

a) lim x ⇒0 eˣ - x - 1cos(x) -1 = -1

b ) q = √a/b

Explanation:

a) lim x ⇒0 eˣ - x - 1cos(x) -1 ⇒ e⁰ -(0) - cos(0) -1 = 1-0-1-1 = -1

B) The weekly cost of the company is C(q) = a/q + bq

In cost equation the term a/q represent the ordering cost. In fact if q increase the ratio a/q decrece and the term bq represent the storage cost that will grow as the storage quantity increase

C(q) = a/q + bq Taking derivative C´(q) = -a/q² + b

-a/q² = -b ⇒ a/q² = b ⇒ q² = a/b ⇒ q = √a/b