Question 1167566
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Let the square base have side x.<br>
Then, since the volume is 36, the height of the box is 36/x^2.<br>
The top and bottom each have area x^2; each side has area x(36/x^2) = 36/x.<br>
The cost is 18 cents per unit area for the bottom, 12 cents per unit area for the four sides, and 14 cents per unit area for the top.  The total cost is<br>
{{{32(x^2)+4(12)(36/x) = 32x^2+1728/x}}}<br>
Use calculus (tedious) or a graphing calculator (fast) to find that the minimum cost is when x=3; then use that to answer the question.<br>