document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197717>Question 1197717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PART 1<BR>\n" );
document.write( "A University has a printer system designed for profit. The printer has a flat cost of $50 every month to run, and it costs the university two cents for every page printed. The university sells each printed page for 10 cents. <BR>\n" );
document.write( "a.	Write an equation to describe the relationship between:<BR>\n" );
document.write( "i) the costs (C) and the number of pages (p)<BR>\n" );
document.write( "ii) income (I) and the number of pages (p)<BR>\n" );
document.write( "b.	Draw a graph to represent the costs and income monthly.<BR>\n" );
document.write( "c.	How many pages need to be sold to break even every month?<BR>\n" );
document.write( "d.	Check your answer to part C algebraically.\r<BR>\n" );
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document.write( "PART 2 \r<BR>\n" );
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document.write( "A company makes and sells fidget spinners. They are sold on eBay for $8 each.<BR>\n" );
document.write( "Using spreadsheet or Desmos, make a table of values showing the income (I) for different quantities sold (n).\r<BR>\n" );
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document.write( "The fixed over-head expenses or Desmos, make a table of values for the number sold against the cost to produce this number of fidget spinners.\r<BR>\n" );
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document.write( "a.	What is the break-even point?<BR>\n" );
document.write( "b.	What does this mean in terms of the number of fidget spinners and the cost/income?<BR>\n" );
document.write( "c.	What is the slope of the income line?<BR>\n" );
document.write( "d.	What is the Income equation (I) if n is the number of fidget spinners sold?<BR>\n" );
document.write( "e.	What is the slope of the cost line?<BR>\n" );
document.write( "f.	What is the Cost equation (C) if n is the number of fidget spinners sold (remember to add in the fixed costs)?<BR>\n" );
document.write( "g.	If the fixed costs of $515 were reduced, with everything else remaining equal, describe how the break-even point would change (in relation to the graph)?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848350 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ### Part 1: University Printer System\r<BR>\n" );
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document.write( "#### a. Write equations<BR>\n" );
document.write( "- **i) Cost equation \(C(p)\):** <BR>\n" );
document.write( "  The cost includes a flat fee of $50 and 2 cents per page:<BR>\n" );
document.write( "  \[<BR>\n" );
document.write( "  C(p) = 50 + 0.02p<BR>\n" );
document.write( "  \]\r<BR>\n" );
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document.write( "- **ii) Income equation \(I(p)\):**<BR>\n" );
document.write( "  The income comes from selling pages at 10 cents per page:<BR>\n" );
document.write( "  \[<BR>\n" );
document.write( "  I(p) = 0.10p<BR>\n" );
document.write( "  \]\r<BR>\n" );
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document.write( "#### b. Graph of Costs and Income<BR>\n" );
document.write( "- The cost graph \(C(p)\) is a straight line starting at $50 with a slope of \(0.02\).<BR>\n" );
document.write( "- The income graph \(I(p)\) is a straight line starting at $0 with a slope of \(0.10\).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Let me know if you'd like a plotted graph.\r<BR>\n" );
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document.write( "#### c. Break-Even Point<BR>\n" );
document.write( "To break even, the income equals the cost:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "C(p) = I(p)<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "50 + 0.02p = 0.10p<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### d. Solve Algebraically<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "50 = 0.10p - 0.02p<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "50 = 0.08p<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "p = \frac{50}{0.08} = 625<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "Thus, **625 pages need to be sold to break even.**\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Part 2: Fidget Spinner Company\r<BR>\n" );
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document.write( "#### Create Tables<BR>\n" );
document.write( "- **Income \(I(n)\):** Income per fidget spinner is $8.<BR>\n" );
document.write( "  \[<BR>\n" );
document.write( "  I(n) = 8n<BR>\n" );
document.write( "  \]\r<BR>\n" );
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document.write( "- **Cost \(C(n)\):** Cost includes fixed overhead of $515 and variable costs:<BR>\n" );
document.write( "  Let me know the variable cost per spinner for precise calculations.\r<BR>\n" );
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document.write( "#### a. Break-Even Point<BR>\n" );
document.write( "To find the break-even point:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "I(n) = C(n)<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "Substitute the income and cost equations and solve for \(n\).\r<BR>\n" );
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document.write( "#### b. Interpretation of Break-Even<BR>\n" );
document.write( "The break-even point represents the number of fidget spinners that must be sold for the income to cover the costs. At this point:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Income = Costs}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### c. Slope of Income Line<BR>\n" );
document.write( "The slope of the income line represents the rate at which income increases per unit sold:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Slope of Income} = 8<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### d. Income Equation<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "I(n) = 8n<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### e. Slope of Cost Line<BR>\n" );
document.write( "The slope of the cost line represents the rate at which cost increases per unit produced:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Slope of Cost} = \text{Variable Cost (value needed)}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### f. Cost Equation<BR>\n" );
document.write( "If the fixed cost is $515 and the variable cost per spinner is \(c\):<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "C(n) = 515 + cn<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "#### g. Effect of Reduced Fixed Costs<BR>\n" );
document.write( "Reducing the fixed costs would lower the \(y\)-intercept of the cost line, shifting it downward. The break-even point would decrease, meaning fewer spinners need to be sold to cover the costs. </SPAN>\n" );
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