SOLUTION: A rectangular bin with an open top and volume of 38.72 cubic feet is to be built. The length of its base must be twice the width and the bin must be at least 3 feet high. Material

Question 1132560: A rectangular bin with an open top and volume of 38.72 cubic feet is to be built. The length of its base must be twice the width and the bin must be at least 3 feet high. Material for the base of the bin costs $12 per square foot. If it costs $538.56 to build the bin, what are its dimensions?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Data:
width=
lenght=
height=

Therefore:

Area of the base:
Area of the base=
Cost of the base=
Area of the sides=
Area of the sides=
Cost of the sides=

Therefore:
Cost of the base + cost of the sides=
=>
We have this system of equations:

We can solve this system of equations by substitution method:

and

I have solved this equation graphically and the result would be:
Solutions:
≈
≈
≈ -> disregard negative solution
check:
≈

This value is not correct , because "y" would be <

And
≈

This value is correct, if "y" is at least ft high.
Therefore:
width=
lenght=

Answer: it´s dimensions would be:

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