A professor wishes to develop a numerical method for giving grades. He intends to base the grade on homework, two midterms, a project, and a final examination. He wishes the final exam to have the largest influence on the grade. He wants the project to have 20%, each midterm to have 10%, and the homework to have 10% of the influence on the semester grade. Required:
a. Determine the weights the professor should use to produce a weighted average for grading purposes.
b. Calculate an (un-weighted) average of these five scores and discuss why the weighted average would be preferable here.