QuestionA mechanic earns \ $14/hour regular and \$21/hour overtime. Find$ W(30), W(40), W(45), W(50)$.

Studdy Solution

STEP 1

Assumptions1. The mechanic's regular hourly wage is $14.00. . The mechanic's overtime wage is time-and-a-half, or1.5 times the regular wage.<br />3. The weekly wage function is given by$ $W(h)=\left\{\begin{array}{ll} 14h, &0<h \leq40 \\ 21(h-40)+560, & h>40 \end{array}\right.$ $where$ h$ is the number of hours worked in a week.

STEP 2

First, we will evaluate $W(30)$ using the first part of the function, since30 hours is less than or equal to40 hours.
$W(30) =14 \times30$

STEP 3

Calculate the weekly wage for30 hours.
$W(30) =14 \times30 = \$420$

STEP 4

Next, we will evaluate $W(40)$ using the first part of the function, since40 hours is less than or equal to40 hours.
$W(40) =14 \times40$

STEP 5

Calculate the weekly wage for40 hours.
$W(40) =14 \times40 = \$560$

STEP 6

Now, we will evaluate $W(45)$ using the second part of the function, since45 hours is greater than40 hours.
$W(45) =21 \times (45 -40) +560$

STEP 7

Calculate the weekly wage for45 hours.
$W(45) =21 \times5 +560 = \$665$

STEP 8

Finally, we will evaluate $W(50)$ using the second part of the function, since50 hours is greater than40 hours.
$W(50) =21 \times (50 -40) +560$

STEP 9

Calculate the weekly wage for50 hours.
$W(50) =21 \times +560 = \$770$ So, the mechanic's weekly wages for30,40,45, and50 hours are $420,$ 560, $665, and$ 770 respectively.

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