MAT 271 Name: Optimization Show all work for full credit. Clearly mark answers. Include units where appropriate. Round final answers only to the nearest hundredths place when necessary 1. Suppose a rectangular pasture is to be constructed using = linear mile of fencing. The pasture will have one divider parallel to one pair of sides and three dividers parallel to the other pair of sides, so that there are eight congruent enclosures. What is the maximum total area of such a pasture, in square feet? Step 1: Draw a picture of the pasture. Label any relevant dimensions in the picture with appropriate variables. Step 2: State the objective quantity (the quantity that must be minimized or maximized), assign a variable to it, and construct a formula for it. State the constraint equation, which should involve all of the variables in the formula Step 3: Solve the constraint for one of the variables (or a piece of the objective quantity) and use this relationship to rewrite the objective quantity as a function of one variable. State the domain of the objective function. Step 4: Differentiate the objective function, set the derivative equal to 0 and solve to determine the critical points of the objective function. Check with the domain of the objective function. Step 5: Use the First Derivative Test or Second Derivative Test to determine the critical point(s) which optimize the objective function. Then answer the question in a complete sentence