document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174253>Question 1174253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The unit cost per gizmo is $30,the fixed cost for making gizmos is $1,200. 60 gizmos must be sold in order to break even.<BR>\n" );
document.write( "-Find linear cost function<BR>\n" );
document.write( "-Find linear revenue function<BR>\n" );
document.write( "-Find linear profit function<BR>\n" );
document.write( "Show work with all steps </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850700 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Linear Cost Function (C(x))**\r<BR>\n" );
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document.write( "* **Fixed Cost:** $1,200<BR>\n" );
document.write( "* **Unit Cost:** $30 per gizmo<BR>\n" );
document.write( "* **x:** Number of gizmos produced\r<BR>\n" );
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document.write( "The linear cost function is the sum of the fixed cost and the variable cost (unit cost multiplied by the number of gizmos):\r<BR>\n" );
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document.write( "   * C(x) = Fixed Cost + (Unit Cost * x)<BR>\n" );
document.write( "   * C(x) = 1200 + 30x\r<BR>\n" );
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document.write( "**2. Linear Revenue Function (R(x))**\r<BR>\n" );
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document.write( "* **Break-even Point:** 60 gizmos<BR>\n" );
document.write( "* At the break-even point, total revenue equals total cost.\r<BR>\n" );
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document.write( "First, let's find the total cost at the break-even point:\r<BR>\n" );
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document.write( "   * C(60) = 1200 + 30(60)<BR>\n" );
document.write( "   * C(60) = 1200 + 1800<BR>\n" );
document.write( "   * C(60) = 3000\r<BR>\n" );
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document.write( "Since revenue equals cost at the break-even point:\r<BR>\n" );
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document.write( "   * R(60) = 3000\r<BR>\n" );
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document.write( "Now, let's find the selling price per gizmo:\r<BR>\n" );
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document.write( "   * Selling Price = Total Revenue / Number of Gizmos<BR>\n" );
document.write( "   * Selling Price = 3000 / 60<BR>\n" );
document.write( "   * Selling Price = 50\r<BR>\n" );
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document.write( "Therefore, the linear revenue function is:\r<BR>\n" );
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document.write( "   * R(x) = Selling Price * x<BR>\n" );
document.write( "   * R(x) = 50x\r<BR>\n" );
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document.write( "**3. Linear Profit Function (P(x))**\r<BR>\n" );
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document.write( "* Profit is the difference between revenue and cost:\r<BR>\n" );
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document.write( "   * P(x) = R(x) - C(x)<BR>\n" );
document.write( "   * P(x) = 50x - (1200 + 30x)<BR>\n" );
document.write( "   * P(x) = 50x - 1200 - 30x<BR>\n" );
document.write( "   * P(x) = 20x - 1200\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* **Linear Cost Function:** C(x) = 1200 + 30x<BR>\n" );
document.write( "* **Linear Revenue Function:** R(x) = 50x<BR>\n" );
document.write( "* **Linear Profit Function:** P(x) = 20x - 1200<BR>\n" );
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