Question 107995: Minimizing Cost, A company uses the formula C(x)=0.02xSquared - 3.4x + 150 t?o model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its mimimum? What is the unit cost at that level of production?
Haven't got a clue what this problem is asking of me. Please help?
Thank you
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! ): Minimizing Cost, A company uses the formula C(x)=0.02xSquared - 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 mimimum? What is the unit cost at that level of production?
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C(x) = .02x^2 - 3.4x + 150; where x = number of units produced
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Here's a clue:
This is a quadratic equation, if we find the axis of symmetry, we will have the value of x for which the minimum occurs:
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The axis of symmetry: x = -b/(2a): In this equation a=.02 and b=-3.4
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x = -(-3.4)/(2*.02)
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x = +3.4/.04
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x = 85 units for minimum cost
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"Find the unit cost?" Substitute 85 for x in the original equation
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Cost = .02(85^2) - 3.4(85) + 150
Cost = .02(7225) - 289 + 150
Cost = 144.5 - 289 + 150
Cost = $5.50 cost per unit at minimum cost
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How about this? Did we shed some light here?
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