Problema Solution
(1 pt) Suppose C(x)=x2−4x+15 represents the costs, in hundreds, to produce x thousand pens. How many pens should be produced to minimize the cost? What is the minimum cost?
Number of pens to minimize the cost:
Minimum cost:
Answer provided by our tutors
we need to find the minimum of the parabolic function:
C(x)=x^2−4x+15
the quotient in front of x^2 is +1 > 0 thus the function has minimum in its vertex:
(-b/2a, c - b^2/4a)
a = 1, b = -4, c = 15
C min = c - b^2/4a
C min = 15 - (-4)^2/(4*1)
C min = 15 - 4
C min = 11 is the minimum cost
x min = -b/2a
x min = -(-4)/(2*1)
x min = 2
Number of pens to minimize the cost: 2
Minimum cost: 11