A rectangular box is to have a square base and a volume of 50 ft3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 26¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
http://www.jiskha.com/display.cgi?id=1295838408
To find a function that gives the cost of constructing the box in dollars, we need to consider the cost of each component of the box separately and then add them up.
Let's break down the components of the box and their costs:
1. Base: The base is square, so its dimensions are x by x. The area of the base is given by x * x = x^2 square feet. The cost of the material for the base is $0.44 per square foot. Therefore, the cost of the base is 0.44 * x^2 dollars.
2. Sides: The box has four sides, each with a height of x and a length equal to the perimeter of the base, which is 4x. So the area of each side is 4x * x = 4x^2 square feet. The cost of the material for the sides is $0.10 per square foot. Therefore, the cost of the sides is 0.10 * 4x^2 dollars.
3. Top: The top is a square with dimensions x by x. The area of the top is given by x * x = x^2 square feet. The cost of the material for the top is $0.26 per square foot. Therefore, the cost of the top is 0.26 * x^2 dollars.
Now, we can add up the costs of all the components to get the total cost of constructing the box:
Total cost = Cost of base + Cost of sides + Cost of top
Total cost = 0.44x^2 + 0.10 * 4x^2 + 0.26x^2
Total cost = 0.44x^2 + 0.40x^2 + 0.26x^2
Total cost = 1.10x^2
Therefore, the function that gives the cost (in dollars) of constructing the box is f(x) = 1.10x^2.