A 100 inch strip of sheet metal starting out 16 inches wide is to be made into a small open trough (open top and ends) by turning up two sides at right angles to the base. The sides will be the same height, x. If the trough is to have maximum volume, how many inches should be turned up on each side?

4 inches should be turned up on both sides.

Step-by-step explanation:

In order to find this, create a situation in which we give the amount turned up on each side as x. Then give the amount that isn't turned up as 16 - 2x (since 2x is the amount turned up). Now we can find the area by multiplying the 3 measurements.

100 * x * (16 - 2x) = MAX

100 * (16x - 2x^2) = MAX

-200x^2 + 1600x = MAX

Now that we have a quadratic function, we can find the maximum value of x by using the vertex formula for x values (-b/2a).

x = - b/2a

x = - 1600/2 (-200)

x = - 1600/-400

x = 4