150
Chapter 3
Dollar cost of the bottom
Ca -- a(2a)(0.20) = 0.40a
2
Dollar cost of the sides
Cs -- 2(ab)(0.10) + 2(2a)(b)(0.10) ab
The total cost of criterion function
C -- 0.40 a 2 + 0.60 ab
The functional constraint
V = (base) (width) (height) = 3
V = (2a)(a)(b) = 12 ft
3
6
a 2
Now placing the functional constraint into the criterion function
C=0.40a2+O.60ab=O.40a2+ 0.60 a(~2)
3.60
C = 0.40 a 2 +a
To obtain the minimum cost
dC
3.60
--=0.80a
----0
da
a 2
a3_ 3.60
0.80
6
a=l.65ft
b=~7=2.20
So the cheapest tank is 1.65 ft x 3.30 ft x 2.20 ft
Note: This example had a regional constraint because the shape is
specified as a rectangle. Also note that when a, b, c are not specified a definite
relation other than the product is t2 ft 3 yields another solution of a cube
2.29 ft on a side. The functional constraints such as plate stresses due to
monitoring of the tank and discontinuity stresses for the vertical and horizontal plates intersecting are missing. Further note, nothing is stated about
what the tank holds.
EXAMPLE 3.2. Find the value of R for maximum power Fig. 3.1
being transmitted to R.