Kramer M. answered • 10/05/16

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Alright, so this can be pretty confusing because it looks like we'll need to utilize piecewise functions to create correct equation. Also, I'll be using m to represent miles.

C

_{1}= 250 if m<= 200 and 250 + .4(m - 200) if m > 200

C

_{2 }= 326.40 + .25mSo on a)

We plug 600 in for m and use the second equation on C

_{1}because m is greater than 200.C

_{1}= 250 + .4(600-200) = 250 + .4(400)

= 250 + 160

= $410

And,

C

_{2 }= 326.40 + .25(600) = 326.40 + 150

= $476.40

And on b)

There will be a point where these equations cross each other and the second option becomes more economical, the best way to picture is as the place where they meet (or where the two equations are equal to each other)

So, 250 + .4(m-200) = 326.40 + .25m

250 + .4m - 80 = 326.40+ .25m

170 +.4m = 326.40 +.25m

170 +.15m = 326.40

.15m = 156.40

m = 1042.666667 or about 1043 miles.

So C

_{1}is best if m<1043And C

_{2}is best if m>=1043
James S.

10/05/16