document.write( "Question 852341: I am really bad at these types of problems and my teacher is terrible at explaining. Can someone please help me with this one.\r
\n" ); document.write( "\n" ); document.write( "Suppose the revenue and cost function for a company is given by:\r
\n" ); document.write( "\n" ); document.write( " R(q)=-.01q^2+30q+7000
\n" ); document.write( " C(q)=5000+25q
\n" ); document.write( " Respectively.\r
\n" ); document.write( "\n" ); document.write( "a.)Find the profit function.
\n" ); document.write( "b.)How many units do we have to produce and sell to reach max[R].
\n" ); document.write( "c.)What is the max[R]?
\n" ); document.write( "d.)What is the fixed cost?
\n" ); document.write( "e.)What is the variable cost?
\n" ); document.write( "f.)Is the cost function a linear function or a quadratic function?
\n" ); document.write( "g.)What is/are the break-even point(s)?\r
\n" ); document.write( "\n" ); document.write( "I know it's a lot but I would really appreciate the help I'm honestly just not getting this. Please and thank you!
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Algebra.Com's Answer #513316 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
The revenue, \"+R+\", is what you take in
\n" ); document.write( "from selling whatever you're selling
\n" ); document.write( "---------------------------------
\n" ); document.write( "The Cost, \"+C+\", is all of the expenses
\n" ); document.write( "paid out so you can sell your products
\n" ); document.write( "----------------------------------
\n" ); document.write( "The Profit, \"+P+=+R+-+C+\", because if
\n" ); document.write( "Revenue is not greater than Cost, then
\n" ); document.write( "you are losing money
\n" ); document.write( "-----------------------------------
\n" ); document.write( "You are given:
\n" ); document.write( "\"+R%28q%29=-.01q%5E2%2B30q%2B7000+\"
\n" ); document.write( "\"+C%28q%29=5000%2B25q+\"
\n" ); document.write( "According to what I just stated,
\n" ); document.write( "\"+P%28q%29+=+R%28q%29+-+C%28q%29+\"
\n" ); document.write( "----------------------------
\n" ); document.write( "\"+P%28q%29+=+-.01q%5E2%2B30q%2B7000+-+%28+5000+%2B+25q+%29+\"
\n" ); document.write( "\"+P%28q%29+=+-.01q%5E2%2B30q%2B7000+-+5000+-+25q+%29+\"
\n" ); document.write( "\"+P%28q%29+=+-.01q%5E2+%2B+5q+%2B+2000+\" ( profit function )
\n" ); document.write( "--------------------------------------------
\n" ); document.write( "To find \"+R%5Bmax%5D+\", you need to find the point ( q, R ) where
\n" ); document.write( "the function \"+R%28q%29=-.01q%5E2%2B30q%2B7000+\" reaches a peak
\n" ); document.write( "The formula to use is:
\n" ); document.write( "\"+q%5Bmax%5D+=+-b%2F%282a%29+\" where:
\n" ); document.write( "\"+b+=+30+\"
\n" ); document.write( "\"+a+=+-.01+\"
\n" ); document.write( "\"+R%28q%29=-.01q%5E2%2B30q%2B7000+\"
\n" ); document.write( "\"+q%5Bmax%5D+=+-30%2F%28+2%2A%28-.01%29%29+\"
\n" ); document.write( "\"+q%5Bmax%5D+=+15%2F.01+\"
\n" ); document.write( "\"+q%5Bmax%5D+=+1500+\"
\n" ); document.write( "1500 units need to be produced to reach \"+R%5Bmax%5D+\"
\n" ); document.write( "-----------------------------------------------
\n" ); document.write( "To find \"+R%5Bmax%5D%2C+plug+this+value+of+%7B%7B%7B+q+\" back into \"+R%28q%29+\"
\n" ); document.write( "\"+R%28q%29=-.01q%5E2%2B30q%2B7000+\"
\n" ); document.write( "\"+R%5Bmax%5D+=+-.01%2A1500%5E2+%2B+30%2A1500+%2B+7000+\"
\n" ); document.write( "\"+R%5Bmax%5D+=+-.01%2A2250000+%2B+45000+%2B+7000+\"
\n" ); document.write( "\"+R%5Bmax%5D+=+-22500+%2B+45000+%2B+7000+\"
\n" ); document.write( "\"+R%5Bmax%5D+=+29500+\"
\n" ); document.write( "The Revenue peaks at $29,500
\n" ); document.write( "-----------------------------
\n" ); document.write( "The cost, \"+C%28q%29+\", is split into:
\n" ); document.write( "\"+25q+\" is variable
\n" ); document.write( "\"+5000+\" is fixed
\n" ); document.write( "--------------------------
\n" ); document.write( "The Cost function is linear because the
\n" ); document.write( "highest power that \"+q+\" is raised to in
\n" ); document.write( "\"+C%28q%29+\" is one
\n" ); document.write( "------------------------------------
\n" ); document.write( "The break-even point is where \"+P%28q%29+=+0+\", or
\n" ); document.write( "where the revenue just barely equals the Cost
\n" ); document.write( "so, to find this point, I can say:
\n" ); document.write( "\"+R%28q%29+=+C%28q%29+\", or, whatis the same thing:
\n" ); document.write( "\"+P%28q%29+=+0+\"
\n" ); document.write( "\"+0+=+-.01q%5E2+%2B+5q+%2B+2000+\"
\n" ); document.write( "You can use the quadratic formula:
\n" ); document.write( "\"+q+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"
\n" ); document.write( "\"+a+=+-.01+\"
\n" ); document.write( "\"+b+=+5+\"
\n" ); document.write( "\"+c+=+2000+\"
\n" ); document.write( "\"+q+=+%28+-5+%2B-+sqrt%28+5%5E2+-+4%2A%28-.01%29%2A2000+%29%29+%2F+%282%2A%28-.01%29%29+\"
\n" ); document.write( "\"+q+=+%28+-5+%2B-+sqrt%28+25+%2B+80+%29%29+%2F+%28-.02%29+\"
\n" ); document.write( "\"+q+=+%28+-5+%2B-+sqrt%28+105+%29%29+%2F+%28-.02%29+\"
\n" ); document.write( "\"+q+=+%28+-5+-+10.247+%29+%2F+%28-.02%29+\"
\n" ); document.write( "\"+q+=+15.247+%2F+.02+\"
\n" ); document.write( "\"+q+=+762.35+\"
\n" ); document.write( "This is the number of items sold at the break-even point
\n" ); document.write( "Here are the plots of:
\n" ); document.write( "\"+R%28q%29+\"
\n" ); document.write( "\"+C%28q%29+\"
\n" ); document.write( "\"+P%28q%29+\"
\n" ); document.write( "
\n" ); document.write( "The bottom parabola is the Profit function, and you can
\n" ); document.write( "see that it is zero ( break-even point ) just below where
\n" ); document.write( "Revenue = Cost. \"+P%28+762.35+%29+=+0+\" as you can see
\n" ); document.write( "( unless I miscalculated )
\n" ); document.write( "Hope this helps
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