A contractor is hired to build a rectangular enclosure with an area of 8 square meters. Three sides of the enclosure are to be made of a wood fence, which costs $3 per foot in length. The fourth side is to be made of brick, which costs $9 per foot in length. Find the dimensions of the pen that minimize the total cost of the enclosure, and find this cost.

a.) Draw a picture of the problem and name your variables:

b.) What is the constraint of the problem?

c.) Write the equation we are optimizing (in this case, minimizing)?

d.) Find the critical points of your optimizing equation:

e.) What are the optimal dimensions for the build?