document.write( "Question 1175979: The profit P per day from selling x units of a commodity is given by P=x(200-0.05x). How many units of the commodity must be sold in order to attain the daily maximum profit? What is the daily maximum profit? \n" ); document.write( "
Algebra.Com's Answer #801809 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "P(x) = x(200-0.05x)
\n" ); document.write( "P(x) = 200x-0.05x^2
\n" ); document.write( "P(x) = -0.05x^2 + 200x + 0
\n" ); document.write( "y = -0.05x^2 + 200x + 0 \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The last equation is in the form y = ax^2+bx+c
\n" ); document.write( "where,
\n" ); document.write( "a = -0.05
\n" ); document.write( "b = 200
\n" ); document.write( "c = 0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The parabola opens downward because the leading coefficient a = -0.05 is negative.
\n" ); document.write( "This means the vertex is the highest point where the max profit occurs.
\n" ); document.write( "The vertex is (h,k) such that
\n" ); document.write( "h = -b/(2a)
\n" ); document.write( "h = -200/(2(-0.05))
\n" ); document.write( "h = 2000
\n" ); document.write( "and
\n" ); document.write( "k = P(h)
\n" ); document.write( "k = -0.05h^2 + 200h + 0
\n" ); document.write( "k = -0.05(2000)^2 + 200(2000) + 0
\n" ); document.write( "k = 200,000\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you sell x = 2000 units per day, then you'll reach the max profit of P = 200,000 dollars per day.
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