Question

a box of volume 252 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost.

Answer 1

To minimize the total cost of the box, find the dimensions that minimize the surface area.

Step-by-step explanation:

To minimize the total cost of the box, we need to consider the dimensions that minimize the surface area.

Let's assume the length and width of the square bottom are x meters. The height of the box is then 252 / x² meters.

The cost of the bottom is 40 * x², and the cost of the sides is 30 * (4x * (252 / x²)).

The total cost is the sum of the costs of the bottom and the sides.

To minimize the total cost, we can find the critical points by taking the derivative of the cost function, setting it equal to zero, and solving for x.