Awarehouse 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, of ordering and storage is given by c=aq+bq, where a, 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?

q = sqrt(a/b)

Step-by-step explanation:

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, of ordering and storage is given by C=aq+bq, where a, b are positive constants.

Minimum C?

Why, find where dC/dq is zero.

C = a/q +bq a and b are positive constants,

C = a*q^(-1) +b*q

Differentiate both sides with respect to q,

dC/dq = a[-1 *q^(-2)] +b

dC/dq = -a/(q^2) +b

Make dC/dq zero,

0 = -a/(q^2) +b

a/(q^2) = b

a/b = q^2

q = sqrt(a/b) the value of q that will give minimum C.

It is minimum because the 2nd derivative of C, [2a/(q^3)], is positive