Geometric Optimization

• Feb 19th 2013, 01:58 PM
spyder12
Geometric Optimization
A large bin for holding heavy material must be in the shape of a box with an open top and a square base. The base will cost 7 dollars a square foot and the sides will cost 9 dollars a square foot. If the volume must be 190 cubic feet. Find the dimensions that will minimize the cost of the box's construction.

Base : ____________
Each side : ______________
• Feb 19th 2013, 02:25 PM
HallsofIvy
Re: Geometric Optimization
Since the base is square, the two sides are equal: let "b" represent the length of a side of the base, in feet. Let "h" represent the height of the box, in feet. Then we have a square base, with area \$\displaystyle b^2\$ square feet and four sides with area bh square feet. Since "the base will cost 7 dollars a square foot and the sides will cost 9 dollars a square foot" the base will cost \$\displaystyle 7b^2\$ dollars and each of the four sides will cost \$\displaystyle 9bh\$ dollars so the total cost is \$\displaystyle 7b^2+ 36bh\$ dollars. That is the function you want to minimize.

Since you did not show any attempt yourself to do this problem, or tell us what methods you have learned to find "minimum" values of a function, I don't know how to tell you to continue.