SOLUTION: an open tank with square bases is to have a volume of 10 cu. m. the materials for its bottom is to cost P15.00 per square meter and that for the sides P6.00 per square meter . find

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Question 720182: an open tank with square bases is to have a volume of 10 cu. m. the materials for its bottom is to cost P15.00 per square meter and that for the sides P6.00 per square meter . find the most economical dimension for the tank
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an open tank with square bases is to have a volume of 10 cu. m.
the materials for its bottom is to cost P15.00 per square meter and that
for the sides P6.00 per square meter .
find the most economical dimension for the tank
:
let x = one side of the square base
let h = the height of the open box
:
The volume
x^2*h = 10
h = 10%2Fx%5E2
:
The surface area cost
Bottom: 15x^2
4sides: 6(4xh) = 24xh
:
Total cost (c)
c = 15x^2 + 24xh
replace h with 10%2Fx%5E2
c = 15x^2 + 24x*10%2Fx%5E2
Cancel
c = 15x^2 + 2410%2Fx
c = 15x^2 + 240%2Fx
Graphing this would be the easiest way to find minimum cost
+graph%28+300%2C+200%2C+-2%2C+8%2C+-50%2C+300%2C+15x%5E2%2B%28240%2Fx%29%29+
minimum cost when x=2 meters is the side of the square base
find the height
h = 10%2F2%5E2
h = 2.5 meters is the height