Suppose we want to build a rectangular storage container with open top whose volume is $$12 cubic meters. assume that the cost of materials for the base is$$‍12 dollars per square meter, and the cost of materials for the sides is $$8 dollars per square meter. the height of the box is three times the width of the base. what’s the least amount of money we can spend to build such a container?

w = w    L = 2w    h = h

Volume:     V = Lwh

                 10 = (2w)(w)(h)

                 10 = 2hw^2

                   h = 5/w^2

Cost:    C(w) = 10(Lw) + 2[6(hw)] + 2[6(hL)])

                      = 10(2w^2) + 2(6(hw)) + 2(6(h)(2w)

                      = 20w^2 + 2[6w(5/w^2)] + 2[12w(5/w^2)]

                      = 20w^2 + 60/w + 120/w

                      = 20 w^2 + 180w^(-1)

            C'(w) = 40w - 180w^(-2)

Critical numbers:

          (40w^3 - 180)/w^2 = 0

                      40w^3 -180 = 0

                              40w^3 = 180

                                  w^3 = 9/2

                                      w = 1.65 m

                                       L = 3.30 m

                                       h = 1.84 m

Cost:  C = 10(Lw) + 2[6(hw)] + 2[6(hL)])

              = 10(3.30)(1.65) + 2[6(1.84)(1.65)] + 2[6(1.84)(3.30)])

              = $165.75                       cheapest cost

Step-by-step explanation:

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

one set of data has more variation than the other. hope this !