To minimize the production cost of the can, we need to find the dimensions that minimize the surface area. The cost can be calculated using the surface area equation for the can.
To minimize the production cost of the cylinder-shaped can, we need to find the dimensions that minimize the surface area of the can.
Let's denote the radius of the can as 'r' and the height of the can as 'h'.
The volume of the can is given as 350 cubic centimeters, so we have the equation:
350 = πr²h
To minimize the surface area, we need to minimize the cost of the material used.
The cost of the material for the sides of the can is 0.02 cents per square centimeter, and the cost for the top and bottom is 0.07 cents per square centimeter.
The total cost can be calculated using the surface area equation for the can:
Cost = 2(πr²) + 2(πrh) + 2(πr²) * 0.07
We can substitute the volume equation into the cost equation and solve for the dimensions that minimize the cost.