1. Jaylen is a basketball player. His success rate (i.e., shooting percentage) when he takes x...

 

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1. Jaylen is a basketball player. His success rate (i.e., shooting percentage) when he takes x two-point attempts is 71-ax. When taking y three-point attempts, his shooting percentage is 54-by. Jaylen will take S shot attempts (i.e., x+y = S), and he will maximize the expected number of points scored. Assume that a, b, and S are positive constants. (i) Find the optimal values of x and y. Your answer will be expressed in terms of a, b, and S. (ii) Suppose that a = b = 2 and S = 20. Find the optimal values of x and y. (iii) Find the expected number of points from a single two-point shot attempt in (ii). Find the expected number from a single three-point attempt. Why should Jaylen not take any more three-point attempts (and correspondingly fewer two-point attempts)? 1. Jaylen is a basketball player. His success rate (i.e., shooting percentage) when he takes x two-point attempts is 71-ax. When taking y three-point attempts, his shooting percentage is 54-by. Jaylen will take S shot attempts (i.e., x+y = S), and he will maximize the expected number of points scored. Assume that a, b, and S are positive constants. (i) Find the optimal values of x and y. Your answer will be expressed in terms of a, b, and S. (ii) Suppose that a = b = 2 and S = 20. Find the optimal values of x and y. (iii) Find the expected number of points from a single two-point shot attempt in (ii). Find the expected number from a single three-point attempt. Why should Jaylen not take any more three-point attempts (and correspondingly fewer two-point attempts)?

Answer rating: 100% (QA)

i x 71aS 54bS 54b 71a54 71 y 71aS 54bS 71a 54b54 71 ii The optimal v... View the full answer