Optimization Worksheet 3.6 With Answers - Calculus Maximus Page 7
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10Calculus Maximus
WS 3.6: Optimization
13. Farmer Tate’s apple orchard now has 30 trees per acre, and the average yield is 400 apples per tree.
For each additional tree that he plants per acre, the average yield per tree is reduced by approximately
10 apples. How many trees per acre will give Farmer Tate the largest crop of apples?
14. A Norman window has a lower section in the shape of a rectangle and an upper portion in the shape of
a semicircle mounted on the upper side of this rectangle. If the window is to be surrounded by 10 feet
of metal border (not including the part connecting the rectangle to the semi-circle), find the ratio of the
overall height to the overall width if the total area of the window is to be a maximum.
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