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Choose the scales so that the feasible region is shown fully within the grid.(if necessary, draft it out on a graph paper first.) Shade out all the unwanted regions and label the required region It also possible to test the vertices of the feasible region to find the minimum or maximum values, instead of using the linear objective function.
Linear Programming Solved Problems
Find x and y so that P = 2 x 3 y is maximum under the conditions \[ \begin \ x \ge 0 \ \ x \ge 0 \ \ x y \le 2000 \ \ 8 x 14 y \le 20,000 \ \end \] .A farmer plans to mix two types of food to make a mix of low cost feed for the animals in his farm.A bag of food A costs and contains 40 units of proteins, 20 units of minerals and 10 units of vitamins.In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost.However, there are constraints like the budget, number of workers, production capacity, space, etc.The following videos gives examples of linear programming problems and how to test the vertices.Several word problems and applications related to linear programming are presented along with their solutions and detailed explanations.A bag of food B costs and contains 30 units of proteins, 20 units of minerals and 30 units of vitamins.How many bags of food A and B should the consumed by the animals each day in order to meet the minimum daily requirements of 150 units of proteins, 90 units of minerals and 60 units of vitamins at a minimum cost?Vertices of the solution set: A at (0 , 0) B at (0 , 1429) C at (1333 , 667) D at (2000 , 0) Calculate the total profit P at each vertex P(A) = 2 (0) 3 ()) = 0 P(B) = 2 (0) 3 (1429) = 4287 P(C) = 2 (1333) 3 (667) = 4667 P(D) = 2(2000) 3(0) = 4000 The maximum profit is at vertex C with x = 1333 and y = 667.Hence the store owner has to have 1333 toys of type A and 667 toys of type B in order to maximize his profit. It takes 2 hours to produce the parts of one unit of T1, 1 hour to assemble and 2 hours to polish.