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QuestionA mechanic earns \14/hourregularand$21/hourovertime.Find14/hour regular and \$21/hour overtime. Find W(30),, W(40),, W(45),and, and W(50)$.
(b) What is the new wage function if the work week is 36 hours?
(c) If pay is \$16/hour for 40 hours, what is the new wage function?

Studdy Solution

STEP 1

Assumptions1. The mechanic's pay is 14.00perhourforregulartime..Theovertimepayistime−and−a−half,whichmeansit′s1.5timestheregularpay.<br/>3.Theweeklywagefunctionisdefinedas14.00 per hour for regular time. . The overtime pay is time-and-a-half, which means it's1.5 times the regular pay.<br />3. The weekly wage function is defined as W(h),where, where h$ is the number of hours worked in a week.
4. The regular work week is40 hours.

STEP 2

To evaluate W(30)W(30), we need to use the first part of the function definition, because30 hours is less than or equal to40 hours.W(30)=14×30W(30) =14 \times30

STEP 3

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

STEP 4

To evaluate W(40)W(40), we use the first part of the function definition, because40 hours is less than or equal to40 hours.
W(40)=14×40W(40) =14 \times40

STEP 5

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

STEP 6

To evaluate W(45)W(45), we use the second part of the function definition, because45 hours is greater than40 hours.
W(45)=21×(45−40)+560W(45) =21 \times (45 -40) +560

STEP 7

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

STEP 8

To evaluate W(50)W(50), we use the second part of the function definition, because50 hours is greater than40 hours.
W(50)=21×(50−40)+560W(50) =21 \times (50 -40) +560

STEP 9

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

STEP 10

For part (b), if the company decreases the regular work week to36 hours, the new weekly wage function becomesW(h)={14h,0<h≤3621(h−36)+504,h>36W(h)=\left\{\begin{array}{ll} 14 h, &0<h \leq36 \\ 21(h-36)+504, & h>36\end{array}\right.

STEP 11

For part (c), if the company increases the mechanic's pay to 16.00perhour,thenewweeklywagefunctionbecomes16.00 per hour, the new weekly wage function becomesW(h)={16h,0<h≤4024(h−40)+640,h>40W(h)=\left\{\begin{array}{ll} 16 h, &0<h \leq40 \\ 24(h-40)+640, & h>40\end{array}\right. $

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