Problema Solution
A manufacturer of brand A jeans has daily production costs of C=0.3x^2-114x+11,420, where C is the total cost (in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize costs? What is the minimum daily cost?
Answer provided by our tutors
we need to find the minimum of the parabolic function
C(x) = 0.3x^2-114x+11420
C min = c - b^2/(4a) where a = 0.3, b = -114, c = 11420
C min = 11420 - (-114)^2/(4*(0.3))
C min = $590
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we need to find x such that C(x) = 590 that is
0.3x^2-114x+11420 = 590
0.3x^2-114x+10830 = 0 divide both sides by 0.3
x^2 - 380x + 36100 = 0
by solving the equation we find
x = 190 jeans
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to minimize the cost there should be 190 jeans produced each day.
the minimum daily cost is $590.