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QuestionA mechanic earns \$14/hr, with overtime at time-and-a-half. Find wages for 30, 40, 45, and 50 hours. New functions for 36 hrs and \$16/hr?

Studdy Solution

STEP 1

Assumptions1. The mechanic's regular pay is 14.00perhour..Overtimepayistime−and−a−halfoftheregularpay.<br/>3.Theweeklywagefunctionisgivenas14.00 per hour. . Overtime pay is time-and-a-half of the regular pay.<br />3. The weekly wage function is given as W(h)={14h,0<h≤4021(h−40)+560,h>40W(h)=\left\{\begin{array}{ll} 14h, &0<h \leq40 \\ 21(h-40)+560, & h>40 \end{array}\right.<br/>4.Thevariable<br />4. The variable h$ represents the number of hours worked in a week.

STEP 2

We need to evaluate the weekly wage function at h=30h=30, h=40h=40, h=45h=45, and h=50h=50. We start with h=30h=30.

STEP 3

Substitute h=30h=30 into the weekly wage function.
w(30)=14×30w(30) =14 \times30

STEP 4

Calculate the value of w(30)w(30).
w(30)=14×30=$420w(30) =14 \times30 = \$420

STEP 5

Substitute h=40h=40 into the weekly wage function.
w(40)=14×40w(40) =14 \times40

STEP 6

Calculate the value of w(40)w(40).
w(40)=14×40=$560w(40) =14 \times40 = \$560

STEP 7

Substitute h=45h=45 into the weekly wage function.
w(45)=21×(45−40)+560w(45) =21 \times (45-40) +560

STEP 8

Calculate the value of w(45)w(45).
w(45)=21×(45−40)+560=$665w(45) =21 \times (45-40) +560 = \$665

STEP 9

Substitute h=50h=50 into the weekly wage function.
w(50)=21×(50−40)+560w(50) =21 \times (50-40) +560

STEP 10

Calculate the value of w(50)w(50).
w(50)=21×(50−40)+560=$770w(50) =21 \times (50-40) +560 = \$770

STEP 11

The company decreases the regular work week to36 hours. We need to adjust the weekly wage function accordingly.

STEP 12

The new weekly wage function isW(h)={14h,0<h≤3621(h−36)+504,h>36W(h)=\left\{\begin{array}{ll} 14h, &0<h \leq36 \\ 21(h-36)+504, & h>36\end{array}\right.

STEP 13

The company increases the mechanic's pay to 16.00perhour.Weneedtoadjusttheweeklywagefunctionaccordingly.Theovertimepaybecomes16.00 per hour. We need to adjust the weekly wage function accordingly. The overtime pay becomes 24.00 per hour.

STEP 14

The new weekly wage function isW(h)={16h,0<h≤4024(h−40)+640,h>40W(h)=\left\{\begin{array}{ll} 16h, &0<h \leq40 \\ 24(h-40)+640, & h>40\end{array}\right.

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