document.write( "Question 169289: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?
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Algebra.Com's Answer #125452 by jojo14344(1513) $\"\"$ $\"About$

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\n" ); document.write( "So we need to know the $\"cost%3F\"$ and $\"selling%3F\"$ for 130,000 chips then.
\n" ); document.write( "Via the data given, we need to do INTERPOLATION to find the 2 unknowns.
\n" ); document.write( ".
\n" ); document.write( "First, we'll get the $\"cost\"$ .
\n" ); document.write( "Let $\"x=cost\"$ for 130,000 chips:
\n" ); document.write( "Based on Given---> $\"system%28100000=40%2C125000=35%2C130000=x%29\"$
\n" ); document.write( "By Interpolation: $\"%28100000-125000%29%2F%28100000-130000%29=%2840-35%29%2F%2840-x%29\"$
\n" ); document.write( " $\"-25000%2F-30000=5%2F%2840-x%29\"$ , cross multiply
\n" ); document.write( " $\"-1000000%2B25000x=-150000\"$
\n" ); document.write( " $\"25000x=1000000-150000=850000\"$
\n" ); document.write( " $\"cross%2825000%29x%2Fcross%2825000%29=cross%28850000%2934%2Fcross%2825000%29\"$
\n" ); document.write( " $\"x\"$ =$34.00/ea, cost
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\n" ); document.write( "Next for the $\"Selling\"$ price of 130,000 chips based on cost=$34.00/ea:
\n" ); document.write( "Based on Selling Price Given on other Quantities produced, let $\"y=Selling\"$ .
\n" ); document.write( "By Interpolation ---> $\"system%2840=65%2C35=63%2Chighlight%2834%29=y%29\"$
\n" ); document.write( " $\"%2840-35%29%2F%2840-34%29=%2865-63%29%2F%2865-y%29\"$
\n" ); document.write( " $\"5%2F6=2%2F%2865-y%29\"$ , cross multiply
\n" ); document.write( " $\"6%2A2=5%2865-y%29\"$
\n" ); document.write( " $\"12=325-5y\"$
\n" ); document.write( " $\"5y=325-12=313\"$ ----> $\"cross%285%29y%2Fcross%285%29=cross%28313%2962.60%2Fcross%285%29\"$
\n" ); document.write( " $\"y\"$ =$62.60/ea, Selling
\n" ); document.write( ".
\n" ); document.write( "For the $\"Profit=Total+Selling-TotalCost\"$ , working eqn
\n" ); document.write( " $\"TotalSelling=62.60%28130000%29\"$ =$8,138,000.00
\n" ); document.write( " $\"TotalCost=34.00%28130000%29\"$ =$4,420,000.00
\n" ); document.write( "Then Via working eqn,
\n" ); document.write( " $\"Profit=8138000-4420000\"$
\n" ); document.write( " $\"highlight%28Profit%29\"$ =$3,718,000.00 ---> Answer
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo\r
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