Applications (Optimization)

Michigan State University - Diagnostic Exam

4.2

A rectangular pen with a divider is made with 120 ft of fencing. The divider partitions the pen into two equal-sized areas. What is the maximum area of the two pens combined?

a) 1200 ft² b) 900 ft² c) 600 ft² d) 400 ft² e) 150 ft²

Solution:

Let x and y be the dimensions of the pen. Then $3x + 2y = 120 ⇒ y = 60 - 1.5x$ . So the area of the pen is given by quadratic function $A = x ⋅ y = x (60 - 1.5x ) = A(x)$ . Since $A(0) = A (40) = 0$ the axis of symmetry must be $x = 20$ . It follows that the maximum area is $A (20) = 20(60 - 1.5(20)) = 600$ .

Diagnostic:

If you miss this question please review applications of quadratic functions.

Also, see 4.1: Graphing (Quadratic Functions) .

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July 15, 2008