MATH 1550 Chapter : Section 4.7 Optimization Problems
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Example: a box with a square base open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of materials used. V = s2 x h (b/c square box) Materials = s2 + 4sh h = 32000/s2. Materials for the base = per meter2. Materials for the side = per meter2. C = (10)(2w)2 + 6(2wh) + 6(2 x 2wh) W = (3square root of 4. 5) = 1. 65. C(3square root of 4. 5) = 20w2 + (5 x 36)/w. Example: -a rectangular plot of land to be fenced by a farmer. Adjacent to the north wall of a barn (no fence needed) Fence along the west will be shared by his neighbor who will pay half of the cost for that side. Fencing costs per linear foot, and farmer is not willing to spend more than . Find the dimensions of the plot will enclose the most area.
