document.write( "Question 866958: Mrs. Maths research has shown that if 100 apple trees are planted then the annual revenue is $90 per tree. If more trees are planted they have less room to grow and generate fewer apples per tree. As a result the annual revenue per tree is reduced by $0.70 for each additional tree planted. How many trees should be planted to maximize the revenue? Round your answer appropriately \n" ); document.write( "

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If 100 apple trees are planted then the annual revenue is $90 per tree.
\n" ); document.write( " If more trees are planted they have less room to grow and generate fewer apples per tree.
\n" ); document.write( " As a result the annual revenue per tree is reduced by $0.70 for each additional tree planted.
\n" ); document.write( " How many trees should be planted to maximize the revenue?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of trees over 100
\n" ); document.write( "Let y = total revenue from the trees
\n" ); document.write( ":
\n" ); document.write( "y = (100+x)*(90-.70x)
\n" ); document.write( "FOIL
\n" ); document.write( "y = 9000 - 70x + 90x - .70x^2
\n" ); document.write( "A quadratic equation
\n" ); document.write( "y = -.7x^2 + 20x + 9000
\n" ); document.write( "At the axis of symmetry, x gives max revenue
\n" ); document.write( "x = $\"%28-20%29%2F%282%2A-.7%29\"$
\n" ); document.write( "x = 14
\n" ); document.write( "We can say at 114 trees, we will have max revenue
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