Running Track You are part of a committee given the responsibility of determining the dimensions of a rectangular practice field of largest area that is surrounded by a running track that is to be exactly 400 m. Practice Field around but which has a semicircle on each end of the field. a) What is the objective function in this situation? A = b) What limits the size of the practice field? What is the constraint equation? (Hint: set an expression for the track length equal to 400 r c) Use the constraint equation to rewrite the objective function in terms of just one variable. A : What is the domain of this function? d) Use the derivative to determine the dimensions of the practice field, to the nearest hundredth meter, that would have the largest area. Width: Length: e) How does the situation change if you want the dimensions so the entire area surrounded by th track has the largest possible area? Determine these dimensions (show work on another sheet Objective Function: Constraint Equation: Objective Function using one independent variable: Width for maximum area: I enoth for maximum area- 1/2