Chapter 1.6, Problem 43E

a.

To determine

The weekly wages of the number.

Answer to Problem 43E

  $420,560,665,770$ .

Explanation of Solution

Given information:

A mechanic’s pay is $\$14.00$ per hour for regular time and time-and-a-half for overtime. The weekly wages of the function:

  $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 40\\ 21(h-40)+560h>40\end{array}\right\}$

Where, $h$ is the number of hours worked in a week $(a)$ Evaluate $W(30),W(40),W(45),$ and $W(50)$ .

Calculation:

The weekly wages of the function:

  $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 40\\ 21(h-40)+560h>40\end{array}\right\}$

Where, $h$ is the number of hours worked in a week

Find the value of W(30) :

It can be seen that the value of h is $30$ , so that the function used here will be,

  $W(h)=14h$ because it is defined between

  $0<h\le 40$ .

Substitute

  $h=30$ in the function,

  $W(h)=14h$ as shown below,

  $\begin{array}{l}W(30)=14(30)\\ W(30)=420\end{array}$

Thus,

  $W(30)=420$ .

Now, calculate for $W(40)$ .

Thus, it can be seen that the value of h is $40$ ,so the function used here will be,

  $W(h)=14h$ because it is defined between

  $0<h\le 40$ .

Substitute

  $h=40$ in the function,

  $W(h)=14h$ as shown below,

  $\begin{array}{l}W(40)=14(40)\\ W(40)=560\end{array}$

Thus,

  $W(40)=560$ .

To find the value of W(45) :

  $\begin{array}{l}W(45)=21((45)-40)+560\\ =105+560\\ =665\end{array}$

To find the value of W(50) :

  $\begin{array}{l}W(50)=21(10)+560\\ =210+560\\ =770\end{array}$

Thus, the value of the wages are $420,560,665,770$ .

b.

To determine

The new wages function.

Answer to Problem 43E

  $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 45\\ 21(h-45)+630h>45\end{array}\right\}$

Explanation of Solution

Given information:

A mechanic’s pay is $\$14.00$ per hour for regular time and time-and-a-half for overtime. The weekly wages of the function:

  $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 40\\ 21(h-40)+560h>40\end{array}\right\}$

Where, $h$ is the number of hours worked in a week $(b)$ The company increased the regular work week to 45 hours. What is the new weekly wage function?

Calculation:

From the given information, the company increased the regular work week to 45 hours. To find the new weekly wages of the function write the amount paid when

  $h>45$ :

  $\begin{array}{l}21(h-45)+14\cdot 45\\ 21(h-45)+630\end{array}$

Now, write the new wage function:

  $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 45\\ 21(h-45)+630h>45\end{array}\right\}$

Thus, the new wages function $W(h)=\left\{\begin{array}{l}14h,\text{ 0<}h\le 45\\ 21(h-45)+630h>45\end{array}\right\}$ .