Construction Costs The length of a rectangular box is to be twice its width, and its volume is to be 30 ft3. The material for the base costs 30¢/ft2, the material for the sides costs 15¢/ft2, and the material for the top costs 20¢/ft2. Letting x denote the width of the box, find a function in the variable x giving the cost of constructing the box.
To find: The cost function as a variable of for the construction of the box.
The width of the box is and the length of the box is twice the width of the box. The volume of the box is . The cost of material for base is , for the sides is and for the top costs is .
The formula to calculate the volume of the box with length , width and height is,
The length of the box is .
Substitute 30 for , for and for in equation (1) to evaluate .
Area of base of the box is , area of the top of the box is and area of the sides of the box is
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