A salesperson receives a base monthly salary of $250 plus a commission of $4 for each unit sold. if the monthly sales exceed 500 units, the salesperson receives a bonus of $150 plus an additional $2.50 for all units sold in excess of 500 units. (a) formulate the monthly compensation functions=f(x),where s equal the monthly compensation in dollar and x equal the number of units sold per month?
Answers
Given : A salesperson receives a base monthly salary of $250 plus a commission of $4 for each unit sold. If the monthly sales exceed 500 units, the salesperson receives a bonus of $150 plus an additional $2.50 for all units sold in excess of 500 units.
To find : salary function S = f (x) .
Solution:
base monthly salary of $250 plus a commission of $4 for each unit sold.
Let say units sold per month = x
S = Monthly Salary = f(x)
=> f(x) = 250 + 4x x ≤ 500
=> f(x) = 2(2x + 125) x ≤ 500
f(x) = 250 + 4x + 150 + 2.5(500 - x) x > 500
=> f(x) = 400 + 4x + 1250 - 2.5x
=> f(x) = 1650 + 1.5x
=>f(x) = 1.5 (x + 1100)
f(x) = 2(2x + 125) x ≤ 500
1.5 (x + 1100) x > 500
Domain is - x ∈ Integer
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