Asked by jason
3.Suppose C(x) = x^2 -10x+27 represents the costs, in hundreds, to produce x thousand pens.
How many pens should be produced to minimize the cost? What is this minimum cost?
How many pens should be produced to minimize the cost? What is this minimum cost?
Answers
Answered by
Reiny
If you know Calculus:
C' (x) = 2x - 10
= 0 for a min of C(x)
solve 2x-10 - 0
then sub that value of x back into C(x) to find the minimum cost
Non-Calculus:
C(x) is just an upward opening parabola
find its vertex and you have both answers
Do this by
1. completing the square, or
2. using ---- the x of the vertex is -b/(2a) = -(-10)/2 = 5
This should be the same as the Calculus method answer,
find C(5) for the actual minimum cost
C' (x) = 2x - 10
= 0 for a min of C(x)
solve 2x-10 - 0
then sub that value of x back into C(x) to find the minimum cost
Non-Calculus:
C(x) is just an upward opening parabola
find its vertex and you have both answers
Do this by
1. completing the square, or
2. using ---- the x of the vertex is -b/(2a) = -(-10)/2 = 5
This should be the same as the Calculus method answer,
find C(5) for the actual minimum cost
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