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Question 26620: This is a word problem I am struggling with: You've been offered a part time job at a local retailer. You are being offered two different pay options:
Plan A: $18 an hour with overtime (above 20 hours/week) paying time and a half.
Plan B: $20 an hour with no over time.
I need to determine the algebraic formulas for plan A(x),(x being number of hours worked each week)and plan B(x) for a continuous domain of [0,40].
I have managed to figure out the plots for the graph but can't seem to wrap my head around the actual Algebraic formulas.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Plan A: $18 an hour with overtime (above 20 hours/week) paying time and a half.
OK LET HIM WORK FOR X HRS./WEEK
NORMAL RATE =18 $/HR.
O.T.RATE =18*1.5=27 $/HR.
NOW IN THE DOMAIN OF 0 TO 40,COMES THE 20HR/WEEK STANDARD AND BEYOND THAT O.T.RATE.
SO WE NEED TO DIVIDE THE DOMAIN INTO 2 PARTS.
1...0 TO 20 AND 2...>20 TO 40
SO NOW FOR X = 0 TO 20.WE HAVE PAY P AS
P=18X
AND FOR X>20..
WE HAVE NORMAL RATE HRS =20
AND EXCESS RATE HOURS =X-20
SO HIS TOTAL PAY P IS
P=20*18+27*(X-20)...
THIS IS KNOWN AS DEFINING A FUNCTION DIFFERENTLY FOR DIFFERENT ZONES OF DOMAIN.SO WE GOT ....
P=18X....FOR X=0 TO 20....AND
P=360+27(X-20)...FOR X>20...
I THINK NOW YOU CAN DO PLAN B BY YOUR SELF ON THIS BASIS.IF YOU HAVE DIFFICULTY COME BACK.
Plan B: $20 an hour with no over time.
I need to determine the algebraic formulas for plan A(x),(x being number of hours worked each week)and plan B(x) for a continuous domain of [0,40].
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