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

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

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

(b) (4 points) Let  be the length of the side of thesquare yard and  be the radius of the circular yard. Whatis the expression that you want to optimize, in term ofboth  and ?

(c) (4 points) Find an equation relating thevariables  and

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