   Chapter 2, Problem 59RE

Chapter
Section
Textbook Problem

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 determine

To find: The cost function as a variable of x for the construction of the box.

Explanation

Given:

The width of the box is x and the length of the box is twice the width of the box. The volume of the box is 30ft3 . The cost of material for base is 30c/ft2 , for the sides is 15c/ft2 and for the top costs is 20c/ft2 .

Formula used:

The formula to calculate the volume of the box with length L , width B and height H is,

V=L×B×H (1)

Calculation:

The length of the box is 2x .

Substitute 30 for V , 2x for L and x for B in equation (1) to evaluate H .

30=(2x)(x)HH=302x2H=15x2

Area of base of the box is 2x2 , area of the top of the box is 2x2 and area of the sides of the box is 2(2x+x)

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