A rectangular building with a square front is to be constructed of materials that costs 12 dollars per ft^2 for the flat roof, 18 dollars per ft^2 for the sides and the back, and 20 dollars per ft^2 for the glass front. We will ignore the bottom of the building.
(a) If the volume of the building is 5,600 ft^3, what dimensions will minimize the cost of materials? (Round your answers to the nearest hundreth such that the dimensions increase from the smallest to the largest.)

Width of 16.49 ft and a Length of 20.59 ft

Step-by-step explanation:

Volume of the building = 5600 ft³

Volume of the building=lwh

Since, the building has a square square front

Width=Height

Therefore: Volume  = w²l

w²l=5600

Total Surface Area of a Cuboid =2(lw+lh+wh)

Since we are ignoring the bottom of the building, total surface area of the building=Area of Back + Area of Glass Front + Area of Two Other Sides + Area of flat top

=w²+w²+2lw+lw

The materials costs $12 per ft² for the flat roof, $18 per ft² for the sides and the back, and $20 per ft² for the glass front.

Cost of the building=18w²+20w²+2(18)lw+12lw

C(l,w)=30w²+48lw

Recall earlier that we derived:

Therefore:

The minimum costs for the material occurs at the point where the derivative equals zero.

Setting it equal to zero

w=16.49 ft

Recall:

l=20.59 ft

The dimensions that will minimize the cost of the room are: Width of 16.49 ft and a Length of 20.59 ft

$18 was the price of the t-shirt

step-by-step explanation:

answer: 48

just remember to use pemdas:

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