  # A rectangular bin is going to be made with a volume of 646 cm3 . The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.3 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?

Question

A rectangular bin is going to be made with a volume of 646 cm3 . The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.3 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?

check_circleExpert Solution
Step 1

Let the side of square base is x cm and the height of walls is h cm Then volume of rectangular bin is x*x*h, that is( x^2)h , from which , we get h=V/x^2

Area of square base is( x^2) cm^2 and area of four walls is (xh) cm^2.

Therefore total cost of material is shown on board.

Step 2

Now, to get the value of x, for which cost is minimum, we solve dc/dx=0.At this value, the value of  double derivative of c with respect to x is positive , so  C is minimum at x=9.19

Step 3

For this value of x, we calcul...

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