Did you make a sketch?
An open rectangular storage shelter is 4 ft. deep, consisting of
two vertical sides and a flat roof, is attached to an existing structure.
The flat roof is made of aluminum and costs 5 dollars per square foot.
The two sides are made of plywood costing 2 dollars per square foot.
If the budget for the project is $400, determine the dimensions
of the shelter which will maximize the volume.
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The width of the shelter is feet.
The height of the shelter is feet.
The depth of the shelter is 4 feet.
The roof's area is ft².
At $5/ft², its cost is: dollars.
The sides have an area of ft².
At $2/ft², they will cost: dollars.
The total cost is: .
. . Solve for .
The volume of the shelter is: . .
Substitute  into : .
Hence: . is the function you must maximize.