SOLUTION: I am in College Algebra and need some major help. A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs 0
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Question 1099840: I am in College Algebra and need some major help. A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.05 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
Helpful information:
h : height of can, r : radius of can
Volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr
To minimize the cost of the can:
The radius should be________.
The minimum cost should be________cents.
The height should be________. Found 2 solutions by josgarithmetic, htmentor:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! The surface area of the can is
Since , we can solve for h in terms of r:
So, rather than simply minimizing the surface area, we need to minimize the cost
function, since the sides and top/bottom have a different cost per unit area.
Substituting the value of h above, we have:
The cost function will be minimized where
Solving for r, we get:
And therefore
Substituting the values, we get:
r = 4.243 cm
h = 10.608 cm
C = 16.97 cents
etc...
The derivative of the cost function with respect to r is shown below.
The function is zero at r = 4.243 cm
(
