Chapter 1.PS, Problem 1PS

To determine

a)

To write:

The linear equation for your current monthly wage $W_1$ in terms of your monthly sales $S$.

Answer to Problem 1PS

Solution:

$W_1=2000+0.07S$.

Explanation of Solution

Definition:

Graph of linear function:

A function f of the form $f\left(x\right)=mx+b$ is called a linear function. The graph of the equation $y=mx+b$ represents a line with slope m and y-intercept b.

Given:

The monthly salary of salesperson is $\$2000$, plus a commission of $7\%$ of sales.

The salary for new job is $\$2300$ per month, plus a commission of $5\%$ of sales.

Calculation:

From given, it is observed that $b_1=2000$ and $m_1=7\%$. That is, $m_1=0.07$.

Here, the linear equation is, $W_1=m_{1}S+b_1$.

Compute the linear equation for your current monthly wage $W_1$ in terms of your monthly sales $S$ by using the definition mentioned above.

$W_1=2000+0.07S$

Hence, the linear equation for your current monthly wage $W_1$ in terms of your monthly sales $S$ is $W_1=2000+0.07S$.

To determine

b)

To write:

The linear equation for your current monthly wage $W_2$ of your new job offer in terms of the monthly sales $S$.

Answer to Problem 1PS

Solution:

$W_2=2300+0.05S$.

Explanation of Solution

Calculation:

From given, it is observed that $b_2=2300$ and $m_2=5\%$. That is, $m_2=0.05$.

Here, the linear equation is, $W_2=m_{2}S+b_2$.

Compute the linear equation for your current monthly wage $W_2$ in terms of your monthly sales $S$ by using the definition mentioned above.

$W_2=2300+0.05S$

Hence, the linear equation for your current monthly wage $W_2$ in terms of your monthly sales $S$ is $W_2=2300+0.05S$.

To determine

c)

To sketch:

The graph of the two equations $W_1=2000x+0.07S$ and $W_2=2300x+0.05S$ by using the graphing calculator in the same viewing window. Find the point of intersection and explain the representation of the point of intersection.

Answer to Problem 1PS

Solution:

The point of intersection is $\left(15000,3050\right)$.

Both jobs gives the same monthly salary when the sales is equals to $\$15,000$.

Explanation of Solution

Calculation:

From part (a) and (b), the two equations are $W_1=2000+0.07S$ and $W_2=2300+0.05S$.

Draw the graph of the two equations $W_1=2000+0.07S$ and $W_2=2300+0.05S$, it is shown below.

From the above graph, it is observed that the point of intersection is $\left(15000,3050\right)$.

Therefore, both jobs gives the same monthly salary when the sales is equals to $\$15,000$.

To determine

d)

To find:

The salary when the sales is $\$20,000$ per month and explain the salesman need to change job or not.

Answer to Problem 1PS

Solution:

No, the salesman doesn’t change the job because current job pays $3400 per month but new job pays $3300 per month.

Explanation of Solution

Calculation:

Compute the current job salary when the sales is $\$20,000$ per month by substituting $S=20,000$ in $W_1=2000+0.07S$.

$\begin{array}{rll}{W}_1& =& 2000+0.07\left(20,000\right)\\ & =& 2000+1400\\ & =& 3400\end{array}$

Therefore, the current job salary is $3400 when the sales is $\$20,000$ per month.

Compute the new job salary when the sales is $\$20,000$ per month by substituting $S=20,000$ in $W_2=2300+0.05S$.

$\begin{array}{rll}{W}_1& =& 2300+0.05\left(20,000\right)\\ & =& 2300+1000\\ & =& 3300\end{array}$

Therefore, the new job salary is $3300 when the sales is $\$20,000$ per month.

Hence, the salesman doesn’t change the job because current job pays $3400 per month but new job pays $3300 per month.