Labor costs $70/hr, machine time costs $400/hr, and 24 miles of road must be graded. a) State this problem in terms of an objective function and constraint(s). b) Solve this problem by hand using the Lagrange multiplier method. Find the optimal values of L, M, and the Lagrange multiplier. c) Check your answer by enumeration using a programming language (Python) and by using Excel Solver. d) At the last minute, before your total cost estimate must be delivered, you receive a call indicating that there is a mistake, and that 26.5 miles of road will require grading. How can you quickly provide a new estimate without additional calculations? What would your estimate be?