document.write( "Question 136259: Solve the followings : \r
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\n" ); document.write( "\n" ); document.write( "1)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?\r
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\n" ); document.write( "\n" ); document.write( "2)Find the area of a rectangle if three of its corners are (-0.1,-3.4), (-7.9,-3.4), and (-0.1,6.8). \n" ); document.write( "

Algebra.Com's Answer #99836 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I can plot this data on a straight line, otherwise called
\n" ); document.write( "a linear plot. The problem doesn't say I can do this, but
\n" ); document.write( "it doesn't exclude it either, and it's the simplest thing
\n" ); document.write( "to do. I'm going to plot both cost/chip
\n" ); document.write( "and price/chip vs chips produced/wk
\n" ); document.write( "In plotting, the vertical axis is always the data that
\n" ); document.write( "RESULTS when changes are made on the x-axis.
\n" ); document.write( "So, the y-axis is cost/chip and price/chip. The x-axis is chips
\n" ); document.write( "produced/wk. I can plot 2 points for cost and 2 points for price
\n" ); document.write( "which gives me 2 straight lines.
\n" ); document.write( "---------------
\n" ); document.write( "For cost/chip:
\n" ); document.write( "First point:
\n" ); document.write( " $\"x+=+100000\"$
\n" ); document.write( " $\"y+=+40\"$
\n" ); document.write( "Second point:
\n" ); document.write( " $\"x+=+125000\"$
\n" ); document.write( " $\"y+=+35\"$
\n" ); document.write( "---------------
\n" ); document.write( "For price/chip:
\n" ); document.write( "first point:
\n" ); document.write( " $\"x+=+100000\"$
\n" ); document.write( " $\"y+=+65\"$
\n" ); document.write( "Second point:
\n" ); document.write( " $\"x+=+125000\"$
\n" ); document.write( " $\"y+=+63\"$
\n" ); document.write( "---------------
\n" ); document.write( "I use the formula
\n" ); document.write( "

\n" ); document.write( "I'll scale the x-axis so 1 unit = 10000 units
\n" ); document.write( "----------------
\n" ); document.write( "For cost/chip vs production/wk
\n" ); document.write( " $\"%2835+-+40%29+%2F+%2812.5+-+10%29+=+%28y+-+40%29+%2F+%28x+-+10%29\"$
\n" ); document.write( " $\"%28-5%29%2F2.5+=+%28y+-+40%29+%2F+%28x+-+10%29\"$
\n" ); document.write( " $\"%28-2%29%2A%28x+-+10%29+=+y+-+40\"$
\n" ); document.write( " $\"y+=+-2x+%2B+60\"$
\n" ); document.write( "For price/chip vs production/wk
\n" ); document.write( " $\"%2863+-+65%29+%2F+%2812.5+-+10%29+=+%28y+-+65%29+%2F+%28x+-+10%29\"$
\n" ); document.write( " $\"%28-2%29+%2F+2.5+=+%28y+-+65%29+%2F+%28x+-+10%29\"$
\n" ); document.write( " $\"%28-.8%29%2A%28x+-+10%29+=+y+-+65\"$
\n" ); document.write( " $\"y+=+-.8x+%2B+73\"$
\n" ); document.write( "One way to check these lines is to plot them
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-1%2C+20%2C+-5%2C+85%2C+-2x+%2B+60%2C+-.8x+%2B+73%29+\"$
\n" ); document.write( "At 13,000 chips/wk (13 on the graph), the profit is the difference
\n" ); document.write( "in the y-coordinates (price - cost)
\n" ); document.write( "cost:
\n" ); document.write( " $\"y+=+-2x+%2B+60\"$
\n" ); document.write( " $\"y+=+-2%2A13+%2B+60\"$
\n" ); document.write( " $\"y+=+34\"$
\n" ); document.write( "price:
\n" ); document.write( " $\"y+=+-.8x+%2B+73\"$
\n" ); document.write( " $\"y+=+-.8%2A13+%2B+73\"$
\n" ); document.write( " $\"y+=+62.6\"$
\n" ); document.write( "price - cost = $\"62.6+-+34+=+28.6\"$
\n" ); document.write( "The profit at 130,000 chips/wk is $28.60 /chip \n" ); document.write( "

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