Question

he organizers of a Reindeer Exhibit have asked you to build temporary yards for two reindeer; each yard will be surrounded by candy-cane fencing on all sides. The geometrically-minded reindeer only like to stay in square and circular yards; they can stay either together or separately. The organizers prefer not to build two yards of the same shape. Your task is to design yards that satisfy both the organizers and the reindeer: you must use the fencing given to build 1 or 2 yards that are circular or square (if there are two yards they must be different shapes).

The reindeer are most happy when the combined enclosed area of the yard(s) is the greatest possible. You have exactly 150 feet of candy-cane fencing. How will you design the yard(s) to optimize the reindeer’s happiness, under the constraints given?

(a) (3 points) In this problem, do you want to maximize or minimize an area?

(b) (4 points) Let  be the length of the side of the square yard and  be the radius of the circular yard. What is the expression that you want to optimize, in term of both  and ?

(c) (4 points) Find an equation relating the variables  and

(d) (7 points) Use your work from previous parts to design the yard(s) optimally. After your mathematical justification, sketch a picture of your finished set-up, with the dimensions labeled.

Answer 1

Hope this is fine.

Appreciate feedback.