A box with a square base and open too must have a volume of BEDS m3. We 1vvish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only It, the Length of one side of the square base. [Hint: use the volume formula to express the height of the box-z in terms of .13.] Simplify your formula as much as possible. Afar} =i J Next, find the derivative, Alfar}. are] d :| Now, calculate when the derivative equals zero, that is, when ATE} = I]. [Hint: multiply both sides by. 4112.] _ ATE] = I] when .1? = | We next have to make sure that this value of 3 gives a minimum value for the surface area. Let's use the second derivative test. Find Aim]. .413) =i .i Evaluate A'fm] at the iii-value you gave above. For the given cost function C() = 57600 + 200x + x find: a) The cost at the production level 1200 b) The average cost at the production level 1200 c) The marginal cost at the production level 1200 d) The production level that will minimize the average cost e) The minimal average cost