A fence enclosure consists of a rectangle of length L and width 2R, and a semicircle of radius R, as shown in Figure 1. The enclosure is to be built to have an area of 1600 m^{2}. The ratio between 2R and L should be within the range of 0.3< 2R/L < 0.6 . The cost of various fence materials is listed in the following table:
Material A ($/m)
Material B ($/m)
Material C ($/m)
Material D ($/m)
Material E ($/m)
Material F ($/m)
Curved portion
120
122
130
136
140
142
Straight portion
128
(Same materials will be used for both curved and straight portions.)
Develop a Matlab program to find the minimum total cost for the fence. A resolution of 0.01 m for the values of R and L is required. A report should be completed to show problem formulation, programming procedure and result discussions.
Figure: The diagram of the fence enclosure.