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Problem 10

Solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. $\begin{array}{ll}\text { Minimize } & c=0.4 x+0.1 y \\ \text { subject to } & 30 x+20 y \geq 600 \\ & 0.1 x+0.4 y \geq 4 \\ & 0.2 x+0.3 y \geq 4.5 \\ & x \geq 0, y \geq 0\end{array}$

Expert verified

The optimal solution to the given LP problem exists at vertex A, \((x, y) = (15, 6.25)\), with a minimum cost of \(c = 6.625\). The feasible region is not empty, and the objective function is not unbounded.

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Chapter 5

What is a "basic solution"? How might one find a basic solution of a given system of linear equations?

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