Question: A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes

A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam.

Items HW Qu ME FE Scheme I .10 .10 30 .50 Scheme II .10 20 30 .40 Scheme III .15 .15 35 35

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