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Page of16 O 200M + 21. (13 points) The organizers of the annual Toronto Holiday 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 2 yards they must be different shapes). The reindeer are most happy when the combined enclosed area of their yard(s) is the greatest possible. You have exactly 150 feet of candycane fencing. How will you design the yard(s) to optimize the reindeer's happiness, under the constraints given? (a) (2 points) In this problem, do you want to maximize or minimize an area? (Circle one) Maximize Minimize (b) (3 points) Let s be the length of one side of the square yard and r be the radius of the circular yard. What is the expression that you want to optimize, in terms of both T and 3? Expression to optimize: (c) (2 points) Find an equation relating the variables 7' and 3. Relationship between T and s: This Question is continued on the next page Page 10 of 16 ZOOM + k Continuation of Question 21 (d) (6 points) Use your work in the parts above to design the yard(s) optimally. After your mathematical justification, sketch a picture of the finished set-up in the box below, with the dimensions labeled. Draw your Design here