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In this document from math 11012: intuitive calculus, spring 2011, students are asked to find the optimal number of orange trees to plant per acre to maximize the total yield. The problem involves creating expressions for the number of trees per acre and yield per tree based on the given information, then using calculus to find the maximum yield. Suitable for university students taking calculus courses.
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MATH 11012 Intuitive Calculus Spring 2011 Circle one: 8:50 5:30 Ms. Kracht
Name: Quiz Score: /
Show your reasoning. Use standard notation correctly. Simplify your answers. You may NOT share calculators or use a cell phone or any Internet device as a calculator.
Let x be the number of additional trees she plants per acre.
(a) (4 pts) Find an expression in terms of x for the number of trees per acre.
(b) (4 pts) Find an expression in terms of x for the yield per tree.
(c) (4 pts) Write a function Y (x) representing the total yield per acre. Simplify.
(d) (6 pts) Use calculus to find the value of the variable which gives the absolute maximum value of your yield function.
(e) (4 pts) Verify that this is the indeed the absolute maximum on the appropriate interval. Explain!
(f) (3 pts) Answer the question in a complete sentence.