MTH 15
Round-End
Fenced
Enclosure
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
MTH15: Applied Calculus I
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
Given Fenced Enclosure
 Given Parameters
• Total Enclosed Area = 1600
Square Feet (1600 ft2)
• Fence Costs in $/Lineal-Ft
– Straight = 30
– Curved = 40
 Determine Lo-Cost R & L
MTH15: Applied Calculus I
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
Given Fenced Enclosure
 Game Plan
• Solve for COST FUNCTION f(R)
• Solve by BOTH of
– Hand Calculus
 Develop Cost Function
– Use min command on Cost Vector
 Will hunt-down LoCost & Address
MTH15: Applied Calculus I
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
MTH15: Applied Calculus I
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
MTH15: Applied Calculus I
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
MTH15: Applied Calculus I
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
.m File Script
% Bruce Mayer, PE
% ENGR25 * 29Jan11
% P1.20: Rounded-End Fenced Enclosure
% file = P2_20_RoundEnd_FencedEnclosure_1201.m
%
% Guess that Rmin is between 5-30 feet.
%* make ve R-vector with 0.01 ft resolution
R = [5:0.01:30];
%
% Calculate the "Vectorized" Cost using this R-Vector
%* need the DOT on the divide to indicate element-by-element division
C = (25*pi+60)*R + 48000./R;
%
% Make a plot to "EyeBall" Solution
%* convert cost $k for easier interpretation
plot(R,C/1000, 'LineWidth', 2),xlabel('R (ft)'),ylabel('Total Cost
(k$)'), grid
%
disp('showing Cost Plot; hit ANY KEY to Continue')
pause
%
% now use min command to hunt down exactly the minimum within Cost
Vector,C
[Cmin, Kmin] = min(C); % [Value, Address]
%
% Now that we the location of Cmin, We can find Rmin and Lmin at the
SAME
% Location
Rmin = R(Kmin);
%
% Recall from Hand Work => Make an L-Vector
% *Don't forget the DOT on SQUARE or DIVIDE operators
L = (1600 - pi*R.^2/2)./(2*R);
Lmin = L(Kmin);
%
% Now Summarize
disp('---------Answer Below-----------')
disp('Rmin, Lmin in FEET; Cmink in $k')
Rmin
Lmin
Cmink = Cmin/1000
%
% Summarizing Plot
plot(R,C/1000, Rmin, Cmin/1000, 'p', 'LineWidth', 2),xlabel('R
(ft)'),ylabel('Total Cost (k$)'), grid
MTH15: Applied Calculus I
7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
Answer Graphically
11
10
Total Cost (k$)
9
8
7
6
5
5
10
15
20
25
R (ft)
MTH15: Applied Calculus I
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
30
L vs R Plot (for Fun)
160
140
120
L (ft)
100
80
60
40
20
0
5
10
15
20
25
R (ft)
MTH15: Applied Calculus I
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
30
Symbol-Based
Alternative
MTH15: Applied Calculus I
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
MTH15: Applied Calculus I
11
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx
MTH15: Applied Calculus I
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-17a_sec_3-5_Round_End_Fence_Enclosure.pptx