Louisa has earmarked at most $250,000 for investing in two companies involved in the production of renewable energy: Solaron Corporation and Windmill Corporation. She specifies that at least $50,000 must be invested in each company and that the amount invested in Solaron Corporation must not exceed 120% of that invested in Windmill Corporation. (a) Write a system of linear inequalities that gives the restrictions placed upon Louisa's investments. (Let x represent the amount in thousands of dollars that Louisa invests in Solaron Corporation, and let y represent the amount in thousands of dollars she invests in Windmill Corporation.)   (b) Graph the solution set S for the system of linear inequalities found in part (a). (When graphing, let x and y be in thousands of dollars.)   (c) Is it possible for Louisa to invest $190,000 in Solaron Corporation and $60,000 in Windmill Corporation? Prove your assertion.

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