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 $140,000 in Solaron Corporation and $110,000 in Windmill Corporation? Prove your assertion.
Yes, it is possible. A feasible region exists and $(x, y) = (140, 110)$ is in this region.
Yes, it is possible. $140,000 invested in Solaron Corporation and $110,000 invested in Windmill Corporation is less than or equal to the $250,000 Louisa has earmarked
Yes, it is possible. $140,000 invested in Solaron Corporation meets the requirement for the minimum investment amount.
No, it is not possible. $140,000 invested in Solaron Corporation is more than 120% of $110,000 invested in Windmill Corporation.
No, it is not possible. $110,000 is too high of an investment in Windmill Corporation.
