Question #6a90d

1 Answer
May 22, 2017

Answer:

If #60# items per day are produced, the unit cost is minimum, i.e.,

#$400.#

Explanation:

#C(x)=x^2-120x+4000.# Completing the square, we get,

# C(x)=x^2-2*60x+60^2-60^2+4000, i.e., #

# C(x)=(x-60)^2+4000-3600=(x-60)^2+400,#

Since, #AA x in RR, (x-60)^2 >=0, C(x) >=400,# which means that,

The Minimum Unit Cost is #$400.#

Further, for this minimum unit cost, if #x# items per day are produced, then,

#C(x)=400 rArr (x-60)^2+400=400 rArr x=60.#

Thus, if daily #60# items are produced, the unit cost is minimum, i.e.,

#$400.#

Enjoy Maths.!