Texts: 5 Marco is a retail sales clerk who has a commission-based salary. Let P be Marco's total monthly pay, in dollars, and n be the number of watches Marco has sold. Marco cannot earn commission on more than 150 watches each month. Suppose P(n) = 1000 + 20n represents P as a function of n.
a) Determine the input variable and describe what it represents.
Input variable: n
Description: The number of watches Marco has sold.
b) Determine the output variable and describe what it represents.
Output variable: P
Description: Marco's total monthly pay in dollars.
c) Determine the appropriate set of domain values for the given situation.
Domain values: n ∈ [0, 150]
Explanation: Marco cannot earn commission on more than 150 watches, so the domain of the function is restricted to the range of 0 to 150.
d) Determine the appropriate set of range values for the given situation.
Range values: P ∈ [1000, 4000]
Explanation: The total monthly pay, P, can range from $1000 (when no watches are sold) to $4000 (when 150 watches are sold).
e) Solve P(n) = 5000.
Interpret your solution to c) in the context of the given situation.
Solution: There is no solution to P(n) = 5000 within the given domain of n ∈ [0, 150]. This means that Marco cannot earn a total monthly pay of $5000 based on the given commission structure and the maximum number of watches he can sell.