MATH 11012 Intuitive Calculus Spring 2011
Circle one: 8:50 5:30 Ms. Kracht
Name: Quiz Score: /25
Quiz 3: Version A
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.
1. An orange grower finds that if she plants 30 trees per acre, each tree will yield 70 bushels of oranges. She also
estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 5 bushels. We
wish to find how many trees she should plant per acre to maximize her harvest (total yield per acre).
Let xbe the number of additional trees she plants per acre.
(a) (4 pts) Find an expression in terms of xfor the number of trees per acre.
(b) (4 pts) Find an expression in terms of xfor 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.
