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`f(x)={{:(3sin^(-1)x,,x in[0,1]),(-sin^(-1)x,,x in[-1,0)):}` <br> The graph of the function y = f(x) is an shown in the following figure <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_TRI_DPP_5_1_E01_221_S01.png" width="80%"> <br> From the graph f(x) = x has only one solution, x = 0 <br> Range of y = f(x) is `[0, 3pi//2]` <br> For f(x) = k having two solutions, `k in (0, pi//2]` **Introduction**

**Linear programming problems**

**Some definition**

**Mathematical Formulation of Linear programing problem(Example)**

**Optimal Product line problem**

**Diet Problem**

**Transportation problem**

**Feasible solution In feasible solution Feasible region in feasible region**

**Convex set and extreme point value theorem**

**Corner point method**