Math 251 Maple Lab 4 You are encouraged to discuss this assignment with other students and with the instructors, but the work you hand in must be your own. For your personalized data and helpful background material see http://math.rutgers.edu/courses/251/Maple For this lab, the data will consist of an inequality constraint, which implicitly denes a domain D in which the value of a certain constraint function is at most 1, and an objective function. Each of these two functions will be polynomials in four variables (w, x, y, and z). Late submissions will not be accepted. Instructions You are to nd the maximum and minimum value of the objective function in the domain D. You should report the max and min values you nd and, for each, whether it occurs: (i) at a critical point of the objective function within the interior of the domain D, or (ii) on the boundary of D, where the constraint function has value exactly 1. The objective function will have exactly one critical point, and you should report whether or not this point lies inside D. Report also the number of points on the boundary of D given as candidates by the method of Lagrange multipliers. Please use some care in copying the constraint equation and objective function. Some of the formulas will be long and elaborate - this problem is almost real. 1 Math 251 Maple Lab 4 Please hand in the following material, stapled together: (1) A text header showing your name and section number (2) A clear identication in your printout of the critical point of the objective function, together with a determination of whether or not this point lies in D. (3) If the critical point does lie inside D, a determination of the value of the objective function at that point. (4) A clear identication in your printout of the points on the boundary of D which are candidates for points where extrema are achieved. These points will be produced by using Maple to carry out the Lagrange multiplier method on your data, and you should show the necessary Maple instructions of this calculation. Be sure to declare explicitly how many dierent candidates (4-tuples of numbers) there are. (5) Explicit specication of the values of the objective function which are candidates for extreme values, arising from the critical point or from the boundary. (6) The actual maximum and minimum values of the objective function. Clean up your worksheet before printing it by removing any instructions that had errors or were not useful