Following the in-class example on Monday, March 2, suppose you have a $10,500 budget for fencing, and you want to fence in the maximum area in a rectangular goat pasture that must be oriented east/west, north/south. Suppose your land is on a west-facing slope, which means that the cost of is $1.50 per foot for N/S fencing, and it's more costly to install fencing on a slope, so it costs $1.90/foot for E/W fencing. What is the optimal North/South dimension for the pasture, to the nearest 1 foot? Hint: Suggested steps: 1) Carefully set up a total cost equation in terms of variables for the N/S sides of the pasture (you could call that dimension N), and the E/W sides (that you could call W). 2) Solve your cost equation for the non-target dimension (W) in terms of the dimension of interest (N) and the budget parameter. You should have W in terms of N as a variable, and B for any budget, and then you can use the budget given above. 3) Find an equation for area in terms of N, and W(N, B). 4) Find the slope of the area equation by taking the derivative with respect to N. 5) Set the slope equation = 0, and solve for the only variable, N.