document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186827>Question 1186827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good Day,<BR>\n" );
document.write( "I didn't get any response to this question.....The demand function for a tablet is given by the model p=200-16x^2, where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derived when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849370 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=849370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
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document.write( "**1. Define the variables:**\r<BR>\n" );
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document.write( "*   p = price per tablet (dollars)<BR>\n" );
document.write( "*   x = quantity of tablets (millions)\r<BR>\n" );
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document.write( "**2. Given information:**\r<BR>\n" );
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document.write( "*   Demand function: p = 200 - 16x²<BR>\n" );
document.write( "*   Cost per tablet: $50<BR>\n" );
document.write( "*   Profit: $125 million when x = 2.5 million\r<BR>\n" );
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document.write( "**3. Find the profit function:**\r<BR>\n" );
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document.write( "*   Revenue = p * x = (200 - 16x²) * x = 200x - 16x³<BR>\n" );
document.write( "*   Cost = 50 * x<BR>\n" );
document.write( "*   Profit = Revenue - Cost = (200x - 16x³) - 50x = 150x - 16x³\r<BR>\n" );
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document.write( "**4. Set up the equation to solve for x:**\r<BR>\n" );
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document.write( "We know the profit was $125 million when x = 2.5 million. We want to find the other value of x that gives the same profit.\r<BR>\n" );
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document.write( "125 = 150x - 16x³\r<BR>\n" );
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document.write( "**5. Solve for x:**\r<BR>\n" );
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document.write( "16x³ - 150x + 125 = 0\r<BR>\n" );
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document.write( "This is a cubic equation. We already know one root: x = 2.5. We can use this information to factor the equation or use numerical methods (like a calculator or software) to find the other root(s).\r<BR>\n" );
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document.write( "*One way to proceed is to use polynomial division to divide the cubic by (x - 2.5). This will leave you with a quadratic equation which you can then solve using the quadratic formula.*\r<BR>\n" );
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document.write( "Solving the cubic equation (using a calculator or software is the most practical method), we find three roots: x ≈ -3.06, x = 2.5, and x ≈ 3.56.\r<BR>\n" );
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document.write( "**6. Interpret the results:**\r<BR>\n" );
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document.write( "*   x ≈ -3.06: This solution doesn't make sense in our context, as the quantity of tablets cannot be negative.<BR>\n" );
document.write( "*   x = 2.5: This is the given quantity, which we already know yields a profit of $125 million.<BR>\n" );
document.write( "*   x ≈ 3.56: This is the other solution we're looking for.\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "The company could sell approximately 3.56 million tablets to make the same amount of profit ($125 million).<BR>\n" );
document.write( " </SPAN>\n" );
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