Linear Progamming

Linear Programming 1.Review of algebra (graph), Feasible arena =, < and >, downward biased line, upward sloping line, horizontal/vertical line etc. 2. application of Linear programming: Liver Brothers producing more than genius reaping such that few resources atomic number 18 usual and few argon different. Most important policy supply optimal harvest-home mix. We optimize an objective function posit to received constraints. These constraints may be of ? (resources), ? (targets) or = types. 3.Graphic Method launch the spare-time activity problem in a paragraph propose: | irate| Sewing| Finishing| Packaging| Profit/ purse| meter base| 7/10| 1/2| 1| 1/10| 10| Deluxe Bag| 1| 5/6| 2/3| 1/4| 9| Max Time| 630| 600| 708| one century thirty-five| -| 4.Model development companion go forth produce x number of archetype bags and y number of deluxe bags. accusive function: Max = 10x + 9y self-confidence1: All relationships are linear i.e. p rofit-output and input-output) s.t.

7/10x + 1y 630 (hours) raw department --------- 1 1/2x + 5/6y 600 (hours) Sewing department --------- 2 x + 2/3y 708(hours) finishing department --------- 3 1/10x + 1/4y ? one hundred thirty-five (hours) packaging department --------- 4 x ? 0 and y ? 0 assumption 2: Non-negativity constraint Assumption 3: All variables are continuous 5.Solution: Draw graph, identify FR, discipline receding points and enter profit at all corner points and select maximum. optimum sol: (540, 252); =7,668 6.2nd Meth od (Optional): Convert obj.fn into standar! d form (y = mx + c); y = -10/9x + /9 Draw family of gibe lines with 10/9 as slope. Highest line within the operable region will give you optimal point. [Note need to apprise this method] 7. relax: Un-utilized resource LHS = Utilization (U) and RHS = Availability (A) U + S = A (add loosen up on LHS and inequality will be come equality) 7/10x + y + S1 = 630 1/2x + 5/6y + S2 = 600...If you want to get a full essay, order it on our website: OrderCustomPaper.com

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