A manufacturer needs to construct a box with a lid for a special product. The only stipulations are that the volume of the box should be 2000 cubic centimeters and that the box should have a square base. The cost for producing such a box has been determined to be represented by the function $C(x)=\frac{80+0.02 x^{3}}{x}$, where $C(x)$ is the cost of the box in dollars and $x$ is the length of a side of the base in centimeters. Use the graph of $C$ to determine the side length $x$ that will minimize the cost of the box, and determine what this cost will be.
(Hint: Use the window $[0,50]$ by $[0,50]$.)

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The Answer of A manufacturer needs to construct a box with a lid for a special product. The only stipulations are that the volume of the box should be 2000 cubic centimeters and that the box should have a square base. The cost for producing such a box has been determined to be represented by the function $C(x)=\frac{80+0.02 x^{3}}{x}$, where $C(x)$ is the cost of the box in dollars and $x$ is the length of a side of the base in centimeters. Use the graph of $C$ to determine the side length $x$ that will minimize the cost of the box, and determine what this cost will be.
(Hint: Use the window $[0,50]$ by $[0,50]$.)

A Manufacturer Needs to Construct a Box with a Lid C(x)=80+0.02x3xC(x)=\frac{80+0.02 x^{3}}{x}C(x)=x80+0.02x3​

A Manufacturer Needs to Construct a Box with a Lid $C(x)=\frac{80+0.02 x^{3}}{x}$