document.write( "Question 994285: The total profit $P, generated from the production and marketing of n items of a certain product is given by
\n" ); document.write( "P = −10800n − 4 n^3 + 600n^2 −122
\n" ); document.write( "How many items should be made for maximum profit? What is the maximum profit? \r
\n" ); document.write( "\n" ); document.write( "Enter your answers as a list [in square brackets] of the form: [ n, p]
\n" ); document.write( "for some number of items n and profit p\r
\n" ); document.write( "\n" ); document.write( "This is what I have\r
\n" ); document.write( "\n" ); document.write( "P = −10800n − 4 n^3 + 600n^2 −122
\n" ); document.write( "P' = -10800 -12n^2 + 1200n\r
\n" ); document.write( "\n" ); document.write( "-10800 -12n^2 + 1200n = 0
\n" ); document.write( "n = 10, n = 90\r
\n" ); document.write( "\n" ); document.write( "But I am not sure what to do from there?
\n" ); document.write( "Do I sub them in?\r
\n" ); document.write( "\n" ); document.write( "-10800 -12(10)^2 + 1200(10) = 0
\n" ); document.write( "-10800 -12(90)^2 + 1200(90) = 0\r
\n" ); document.write( "\n" ); document.write( "I'm lost!\r
\n" ); document.write( "\n" ); document.write( "Thank you!! \n" ); document.write( "

Algebra.Com's Answer #613451 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
The total profit $P, generated from the production and marketing of n items of a certain product is given by
\n" ); document.write( "P = −10800n − 4 n^3 + 600n^2 −122
\n" ); document.write( "How many items should be made for maximum profit? What is the maximum profit? \r
\n" ); document.write( "\n" ); document.write( "Enter your answers as a list [in square brackets] of the form: [ n, p]
\n" ); document.write( "for some number of items n and profit p\r
\n" ); document.write( "\n" ); document.write( "This is what I have\r
\n" ); document.write( "\n" ); document.write( "P = −10800n − 4 n^3 + 600n^2 −122
\n" ); document.write( "P' = -10800 -12n^2 + 1200n\r
\n" ); document.write( "\n" ); document.write( "-10800 -12n^2 + 1200n = 0
\n" ); document.write( "n = 10, n = 90\r
\n" ); document.write( "\n" ); document.write( "But I am not sure what to do from there?
\n" ); document.write( "Do I sub them in?\r
\n" ); document.write( "\n" ); document.write( "-10800 -12(10)^2 + 1200(10) = 0
\n" ); document.write( "-10800 -12(90)^2 + 1200(90) = 0\r
\n" ); document.write( "\n" ); document.write( "I'm lost!\r
\n" ); document.write( "\n" ); document.write( "Thank you!!
\n" ); document.write( "

You're correct up to this point:  -------> 
\n" );
document.write( "Now, maximum profit (P) is realized at: 
\n" );
document.write( "With b being 1200, and a being - 12,  becomes: , or , or 50
\n" );
document.write( "Number of units at which maximum profit occurs is: \r
\n" );
document.write( "\n" );
document.write( "As mentioned before, this means that maximum profit is realized at n = 50 (I presume this should be in 000s, or millions) units\r
\n" );
document.write( "\n" );
document.write( " -------- Substituting 50 for n
\n" );
document.write( "
\n" );
document.write( "P, or maximum profit = - 30,000 + 60,000 - 10,800, or 
\n" );
document.write( "This results in: [n, P], or [] \n" );
document.write( "

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