please show work

MAT 117- Problem Set 2: Objectives 5-9 2. Hector is building a rectangular shaped dog pen. Hector will use the side of his house as one of the sides of the dog pen, so he only needs to construct three additional sides for the pen. The three sides that Hector needs to construct will be made from mesh fencing that casts $7.25 per foot. He wants the enclosed area to be 5000 square feet. He will also need 4 corner posts costing $8.50 each. Fence x feet 5000 Square Feet x feet Wall or House a. [6 pts] Let x be the length of the side of the dog pen that is perpendicular to his house. Write a function C(x), for the cost of the materials for the pen in terms of x. Simplify your expression by combining any like terms. (Hint: you will have to find a way to express the length of the remaining side in terms of x and the given area of the pen. Also don't forget to incorporate the cost of the fencing AND the cost of the four posts into the formula.) b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0 x