Dimensions of a building?

A small office unit is to contain 500 ft^2500ft2 of floor space.

(a) express the length yy of the building as a function of the width xx

(b) if the walls cost $100$100 per running foot express the cost CC of the walls as a function of the width xx (Disregard the wall space above the doors and the thickness of the walls.)

I figured out (a) to be y(x) = 500/xy(x)=500x

but im having trouble with (b)
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1 Answer
Feb 18, 2018

C=(300x^2-600x+100000)/xC=300x2600x+100000x

Explanation:

.

Your answer to part (a)(a) is correct.

Part (b)(b):

The total length of the walls is the perimeter of the building plus the middle divider but we have to subtract the widths of the two doors.

Let the perimeter be PP and total length of the walls be LL.

P=2(x+y)P=2(x+y)

L=2(x+y)+x-2(3)=2x+2y+x-6L=2(x+y)+x2(3)=2x+2y+x6

L=3x+2y-6L=3x+2y6

Now, we can substitute your answer from part (a)(a) for yy:

L=3x+2(500/x)-6L=3x+2(500x)6

L=3x+1000/x-6L=3x+1000x6

C=100(3x+1000/x-6)C=100(3x+1000x6)

C=300x+100000/x-600=(300x^2-600x+100000)/xC=300x+100000x600=300x2600x+100000x