SOLUTION: 1) Profit per tree grown and sold depends upon the height of tree at the time of sale. Taking h as tree height in metres, profit of tree in thousands Tanzanian shillings is approxi
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-> SOLUTION: 1) Profit per tree grown and sold depends upon the height of tree at the time of sale. Taking h as tree height in metres, profit of tree in thousands Tanzanian shillings is approxi
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Question 1190566: 1) Profit per tree grown and sold depends upon the height of tree at the time of sale. Taking h as tree height in metres, profit of tree in thousands Tanzanian shillings is approximated as: P(h) = (10 + 2h) ^ (1/2) - 0.1h (1) What tree height provides maximum profit per tree? (2) What is the maximum profit per tree? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! your equation is p(h) = (10 + 2h) ^ (1/2) - .1h.
the equation for graphing is y = (10 + 2x) ^ (1/2) - .1x.
for graphing, y takes the place of p(h) and x takes the place of h.
here is a graph of the equation.
the graph shows the maximum profit is 5.5, when h = 45.
i'm not sure how else you would find it unless you used calculus and found the derivative and then set the derivative to 0.
i used a derivative calculator to find the derivative.
the derivative was equal to 1/sqrt(10 + 2x) - .1
i set it to 0 and solved for x.
i got x = 45.
that's the same as i got using the graph.
either way, your maximum profit is at h = 45.
at that point, f(h) = (10 + 2 * 45) ^ 1/2) - .1 * 45 = 5.5.
that means that the greatest profit is 5.5 thousand tanzanian shillings when the tree is 45 meters high.
