document.write( "Question 1128209: Maximum profit: A kitchen appliance manufacturer can produce up to 200 appliances per day. The profit made from the sale of these machines can be modeled by the function P(x)=-0.5x^2+175x-3300 where P(x) is the profit in dollars, and x is the number of appliances made and sold.\r
\n" ); document.write( "\n" ); document.write( "a)Find the y intercept and explain what it means in this context.
\n" ); document.write( "b)Find the x intercepts and explain what they mean in this context.
\n" ); document.write( "c)Determine the domain of the function and explain its significance.
\n" ); document.write( "d)How many should be sold to maximize profit? What is the maximum profit? \n" ); document.write( "

Algebra.Com's Answer #780761 by Shin123(626) $\"\"$ $\"About$

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a) The y intercept occurs when x=0. \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: Completing the Square for Quadratics

To complete the square for the quadratic $\"-0.5%2Ax%5E2%2B175%2Ax-3300=0\"$ , we must first find a square which when expanded, has -0.5x² and 175x in it.
\n" ); document.write( "Factoring -0.5 from the left side gives $\"-0.5%28x%5E2-350%2Ax%2B6600%29=0\"$ . $\"%28x-175%29%5E2\"$ is the square we are looking for. So we get $\"-0.5%28%28x-175%29%5E2-24025%29=0\"$ .\n" ); document.write( "Taking the -24025 out of the -0.5, we get $\"highlight%28-0.5%28x-175%29%5E2%2B12012.5%29\"$ . Subtracting 12012.5 from both sides, we get $\"-0.5%28%28x-175%29%5E2%29=-12012.5\"$ . Since the right side is negative, there are no real solutions.

\n" ); document.write( " Plugging in x=0 gives y=-3300. The y intercept shows the profit if they make no appliances.
\n" ); document.write( "b) From the above, the x-intercepts are x=330 and x=20. The x-intercepts show where they make no profit.
\n" ); document.write( "c) $\"-0.5%28x-175%29%5E2%2B12012.5=0\"$ Since the square of any real number is nonnegative and the square is multiplied by a negative number, the maximum profit occurs when $\"%28x-175%29%5E2=0\"$ . This occurs when x=175. They make 12012.50 dollars if they make 175 appliances. \n" ); document.write( "

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