1. A landscaping company wants to build a rectangular corral with 800 feet of fencing. One side of the corral will be formed by a house, and the corral will be partitioned into 2 equal-sized pieces, using a fence in the middle of the corral perpendicular to the house's wall. Determine the dimensions of the corral that will maximize its area. (a) (4 points) Make a sketch of the corral and label it with appropriate variables. (b) (2 points) Write down the objective function (the function to be maximized). Use the variables from your sketch. (c) (2 points) What is the constraint equation? This is an equation that the variables must satisfy. (d) (2 points) Express the objective function as a function of a single variable. (e) (6 points) Find the dimensions of the corral with maximum area using your objective function in part (d)