Download Project 2 (Spring 2012) Minimum Cost of Shipping Crate with Given

Project 2 (Spring 2012)
Minimum Cost of Shipping Crate with Given Volume
The Project Statement:
Consider a rectangular shipping crate with volume equal to V cubic feet. The sides cost
$S per square foot, the bottom costs $B per square foot, and top costs $T per square foot. If the
base is small, then the height must be large. Or, if the height is small, then the base must be
large. In either extreme, the surface area and resulting cost will increase. Find the dimensions of
the crate so that the cost will be a minimum.
The Math Model:
If the bottom is x by y and the height is z, then
volume = V = (xy)z.
The total cost is the cost of the bottom plus the cost of the four sides plus the cost of the top
total cost = B(xy) + 2(Sxz) + 2(Syz) + T(xy).
The volume equation gives z = V/(xy). The total cost may be expressed as a function of only x
and y
C(x,y) = Bxy + 2SV/y + 2SV/x + Txy.
Methods of Solution:
There are three methods of solution: graph the cost function with mesh(cost matrix) and
contour(cost matrix), use the command min(min(cost matrix)) and use partial derivatives (need
multivariable calculus).
(a). Use the first two methods to find x, y, z and the minimum cost when B = 3, S = 1 and T = 2
with V = 4000.
(b). Repeat part (a) if the price of materials for the bottom increases by 30 percent.
(c). Repeat part (a) if the shipping crate has no top.
Structure of the Report:
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problem or application and objectives (5 points)
model and derivation (5 points)
general description of the Matlab code with inputs B, S, T and V (5 points)
experimentation with parameters of the model (parts (a), (b) and (c))….
include the three models and three executions with graphical outputs (15 points)
Matlab code in a separate file (70 points)
Structure of the Matlab Code:
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documentation header and comment lines (15 points)
inputs section (15 points)
execution section (25 points)
output section (15 points)
Submissions:
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may work in groups of one, two or three
one *.doc or *.docx file with report, include all names in group
one *.m code file that I can execute
electronic via moodle
deadline is 12:05 AM, Wednesday, February 22.