document.write( "Question 1204231: C(x)= 0.1x^2-0.7x+2.425, where C(x) is hundreds of dollars. How many bicycles should be built in order to minimize the average cost per bicycle \n" ); document.write( "
Algebra.Com's Answer #840355 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Based on this previous problem here
\n" ); document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1177138.html
\n" ); document.write( "It appears there should be the instruction that \"x hundred bicycles are built\"\r
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\n" ); document.write( "\n" ); document.write( "x = number of bikes in hundreds
\n" ); document.write( "eg: x = 3 means 300 bikes are made
\n" ); document.write( "C(x) = 0.1x^2-0.7x+2.425 is the cost in hundreds of dollars.\r
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\n" ); document.write( "\n" ); document.write( "\"%28C%28x%29%29%2Fx+=+%280.1x%5E2-0.7x%2B2.425%29%2Fx\" represents the average cost, in hundreds of dollars, of making x hundred bikes.\r
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\n" ); document.write( "\n" ); document.write( "Use calculus or a graphing calculator to determine the local min of \"%28C%28x%29%29%2Fx\"
\n" ); document.write( "GeoGebra and Desmos are graphing tools I recommend.
\n" ); document.write( "If you have a TI83 or TI84, then that works as well.\r
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\n" ); document.write( "\n" ); document.write( "When x > 0, the lowest point happens at roughly (4.92443, 0.28489)\r
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\n" ); document.write( "\n" ); document.write( "x = 4.92443 leads to 100*4.92443 = 492.443\r
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\n" ); document.write( "\n" ); document.write( "Of course it's not possible to build 0.443 of a bike.
\n" ); document.write( "We look at integer values to the left and right of 492.443
\n" ); document.write( "We'll look at integer values 492 and 493 which correspond to x = 4.92 and x = 4.93 respectively.\r
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\n" ); document.write( "\n" ); document.write( "If x = 4.92, then the average cost is:
\n" ); document.write( "\"%28C%28x%29%29%2Fx+=+%280.1x%5E2-0.7x%2B2.425%29%2Fx\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28C%284.92%29%29%2F%284.92%29+=+%280.1%284.92%29%5E2-0.7%284.92%29%2B2.425%29%2F%284.92%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28C%284.92%29%29%2F%284.92%29+=+0.28488617886179\" approximately\r
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\n" ); document.write( "\n" ); document.write( "\"%28C%284.92%29%29%2F%284.92%29+=+0.2849\" approximately\r
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\n" ); document.write( "\n" ); document.write( "Since \"%28C%28x%29%29%2Fx\" is the average cost in hundreds of dollars, it means the result 0.2849 represents 0.2849*100 = 28.49 dollars.
\n" ); document.write( "It costs around 28.49 dollars per bike, on average, if 492 bikes are made.\r
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\n" ); document.write( "\n" ); document.write( "Now try x = 4.93
\n" ); document.write( "\"%28C%28x%29%29%2Fx+=+%280.1x%5E2-0.7x%2B2.425%29%2Fx\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28C%284.93%29%29%2F%284.93%29+=+%280.1%284.93%29%5E2-0.7%284.93%29%2B2.425%29%2F%284.93%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28C%284.93%29%29%2F%284.93%29+=+0.2848864097363\" approximately\r
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\n" ); document.write( "\n" ); document.write( "\"%28C%284.93%29%29%2F%284.93%29+=+0.2849\" approximately
\n" ); document.write( "We get the same average cost as before. \r
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\n" ); document.write( "\n" ); document.write( "It is up to the company to decide whether to make 492 bikes or 493 bikes.
\n" ); document.write( "Either option produces the lowest average cost of $28.49 dollars per bike.
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