The grading of roadways requires both labor and machine time. Assume that from empirical experience, the number of miles of highway H that can be graded as a function of L hours of labor and M hours of machine time is given by: H = 0.0025L1.35 M1.1 Labor costs $70/hr, machine time costs $540/hr, and 25 miles of highway 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 using the 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 highway will require grading. How can you quickly provide a new estimate without re-solving the model? What would your estimate be?
The grading of roadways requires both labor and machine time. Assume that from empirical experience, the number of miles of highway H that can be graded as a function of L hours of labor and M hours of machine time is given by:
H = 0.0025L1.35 M1.1
Labor costs $70/hr, machine time costs $540/hr, and 25 miles of highway 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 using the 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 highway will require grading. How can you quickly provide a new estimate without re-solving the model? What would your estimate be?
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