You are constructing a box for your cat to sleep in. The plush material for the...

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You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs 5 dollars per square foot and the material for the sides costs 3 dollars per square foot. You need a box with volume 4 ft. Use x to represent the length of the square base, and use h to represent the height of the box. (a) Determine a formula for the height h in terms of x. = (b) Determine a formula for the total cost C(x) of the materials for the box. C(x) = (c) Find the dimensions (in ft) of the box that minimize cost. length of the base ft height ft You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs 5 dollars per square foot and the material for the sides costs 3 dollars per square foot. You need a box with volume 4 ft. Use x to represent the length of the square base, and use h to represent the height of the box. (a) Determine a formula for the height h in terms of x. = (b) Determine a formula for the total cost C(x) of the materials for the box. C(x) = (c) Find the dimensions (in ft) of the box that minimize cost. length of the base ft height ft

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a To determine the formula for the height h in terms of x we know that the volume of a box is length ... View the full answer