Question 150353This question is from textbook
: Minimizing cost. A company uses the formula C(x) = 0.02x² - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
This question is from textbook
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Minimizing cost. A company uses the formula C(x) = 0.02x² - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
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Simply by looking at a quadratic equation we can tell whether opens up or down. If it opens down -- the vertex gives you the maximum. If it opens up -- the vertex gives you a minimum.
To do this, consider the general quadratic form:
y = ax^2 + bx + c
You simply need to look at the coefficient of the x^2 term (a) -- if it is positive, it opens up. if it is negative, it opens down.
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Looking at:
C(x) = 0.02x² - 3.4x + 150
the value of 'a' is 0.02 (positive) therefore, the vertex will be a "minimum".
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The x coordinate of the vertex can be found with:
x = -b/2a
x = -(-3.4)/2(.02)
x = (3.4)/(.04)
x = 85
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For what number of bars is the unit cost at its minimum? 85 stabilizer bars
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C(x) = 0.02x² - 3.4x + 150
C(85) = 0.02(85)² - 3.4(85) + 150
C(85) = 144.5 - 289 + 150
C(85) = 5.5
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What is the unit cost at that level of production? $5.50
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