Question: 1. Consider the following linear programming problem: Min s.t. x + 2x, x, + 3x, 390 8x2 + 2x, 2160 3x, + 2x, 2120 X

1. Consider the following linear programming

1. Consider the following linear programming problem: Min s.t. x + 2x, x, + 3x, 390 8x2 + 2x, 2160 3x, + 2x, 2120 X 570 X1, X220 a. Write the problem in standard form. Identify slack/surplus variables. (10 points) b. The optimal solution of the above LP model is (180/7, 150/7). What are the values of the slack and surplus variables at the optimal solution? (12 points) a a a a 3. Innis Investments manages funds for a number of companies and wealthy clients. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. According to Innis's risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. Which is the objective function for this problem? A. Max 8S + 3M B. Max 8S + 3M - 1.2X C. Min 8S + 3M D. Min 8S + 3M - 1.2X - 2. Consider the following linear programming problem: Max s.t. X, + 2x2 X, + x2 53 X; 2x, 20 X

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