By Sanjay Sharma
Sharma S. utilized Nonlinear Programming (New Age foreign (P) Ltd, 2006)(ISBN 812241771X)
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Extra info for Applied nonlinear programming
1 INTRODUCTION In some of the applications, either open or closed containers are fabricated from the sheet metal, which are used for transporting certain volume of goods from one place to another. Cross-section of the container may be rectangular, square or circular. A cylindrical vessel or a container with circular cross-section is shown in Fig. 1. Fig. 1 A cylindrical box. e. without a lid), area of the sheet metal used for bottom = πr2 where r = Radius in m. Considering cost of fabricating including material cost as Rs.
3. 1 in each successive iteration. Solution. 6) is used. S. of the constraints, is multiplied with penalty parameter r, and then this is deducted from function f(X). 7) In order to minimize Φ, this is differentiated partially with respect to x1 and x2, and equated to zero. 9) respectively. 7) in order to get Φ* and similarly f(X) or f(x1, x2) are obtained for decreasing sequence of r. 1, this is multiplied with the previous value of r in each iteration. 1. 59 Values of Φ as well as f are increasing.
Cross-section of the container may be rectangular, square or circular. A cylindrical vessel or a container with circular cross-section is shown in Fig. 1. Fig. 1 A cylindrical box. e. without a lid), area of the sheet metal used for bottom = πr2 where r = Radius in m. Considering cost of fabricating including material cost as Rs. 1) Area of the vertical portion = 2πrh where h = height in m. Considering cost per m2 as Rs. 2) 3 If 90 m of the goods are to be transported, then number of trips needed = 90 πr2h Considering the transportation cost as Rs.
Applied nonlinear programming by Sanjay Sharma