Minimizing construction costs. Denney Construction is planning to build a warehouse whose interior volume is to be 252, 000 ft 3 . Construction costs per square foot are estimated as follows; Walls $3.00 Floor $4.00 Ceiling: $3.00 a. The total cost of the building is C ( x , y , z ) where x is the length, y is the width, and z is the height, all in feet. Find a formula for C ( x , y , z ) . b. What dimensions of the building will minimize the total cost? What is the minimum cost?
Minimizing construction costs. Denney Construction is planning to build a warehouse whose interior volume is to be 252, 000 ft 3 . Construction costs per square foot are estimated as follows; Walls $3.00 Floor $4.00 Ceiling: $3.00 a. The total cost of the building is C ( x , y , z ) where x is the length, y is the width, and z is the height, all in feet. Find a formula for C ( x , y , z ) . b. What dimensions of the building will minimize the total cost? What is the minimum cost?
Solution Summary: The author calculates a formula for the total cost of the building represented by C(x,y,z) where x is length, y is width and z is height.
Minimizing construction costs. Denney Construction is planning to build a warehouse whose interior volume is to be 252, 000
ft
3
. Construction costs per square foot are estimated as follows;
Walls
$3.00
Floor
$4.00
Ceiling:
$3.00
a. The total cost of the building is
C
(
x
,
y
,
z
)
where x is the length, y is the width, and z is the height, all in feet. Find a formula for
C
(
x
,
y
,
z
)
.
b. What dimensions of the building will minimize the total cost? What is the minimum cost?
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