2. benjamin is a commission - based salesperson. his pay structure is: - 16% commission on the first $1,800…

2. benjamin is a commission - based salesperson. his pay structure is: - 16% commission on the first $1,800 profit, - 22% commission on profit from $1,800 to $3,000, - 28% commission on profit above $3,000. in one month, benjamin generated $4,750 in profit. in addition, he contributes 5% of his total commission to retirement. tasks: a) write a piecewise function for benjamins commission c(x). b) calculate his total commission for $4,750 profit. c) find his retirement contribution. d) determine his take - home commission after retirement deduction.

2. benjamin is a commission - based salesperson. his pay structure is: - 16% commission on the first $1,800 profit, - 22% commission on profit from $1,800 to $3,000, - 28% commission on profit above $3,000. in one month, benjamin generated $4,750 in profit. in addition, he contributes 5% of his total commission to retirement. tasks: a) write a piecewise function for benjamins commission c(x). b) calculate his total commission for $4,750 profit. c) find his retirement contribution. d) determine his take - home commission after retirement deduction.

Answer

Explanation:

Step1: Define the piece - wise function

For $0\leq x\leq1800$, $c(x)=0.16x$. For $1800 < x\leq3000$, $c(x)=0.16\times1800 + 0.22(x - 1800)=288+0.22x-396=0.22x - 108$. For $x>3000$, $c(x)=0.16\times1800+0.22\times(3000 - 1800)+0.28(x - 3000)=288+264+0.28x - 840=0.28x - 288$. So, $c(x)=\begin{cases}0.16x, & 0\leq x\leq1800\0.22x - 108, & 1800 < x\leq3000\0.28x - 288, & x>3000\end{cases}$

Step2: Calculate total commission for $x = 4750$

Since $x = 4750>3000$, use $c(x)=0.28x - 288$. $c(4750)=0.28\times4750-288=1330 - 288=1042$.

Step3: Calculate retirement contribution

Retirement contribution is $5%$ of total commission. $0.05\times1042 = 52.1$.

Step4: Calculate take - home commission

Take - home commission is total commission minus retirement contribution. $1042-52.1 = 989.9$.

Answer:

a) $c(x)=\begin{cases}0.16x, & 0\leq x\leq1800\0.22x - 108, & 1800 < x\leq3000\0.28x - 288, & x>3000\end{cases}$ b) $$1042$ c) $$52.1$ d) $$989.9$