Question: 1. Consider the following integer programming problem: Minimize Z = 4x1 + 5x2 subject to 3x1 + 6x2 18 5x1 + 4x2 20 8x1 +

1. Consider the following integer programming problem: Minimize Z = 4x1 + 5x2 subject to 3x1 + 6x2 18 5x1 + 4x2 20 8x1 + 2x2 16 7x1 + 6x2 42 and x1 0 and x2 0, where x1 and x2 are integers (a). Use TORAs graphical method to find the optimal solution to the LP relaxation of this problem. Include a TORA screenshot of this graphical solution. (b). Round your values of x1 and x2 from your answer to part (a) to obtain a feasible rounded solution to the integer programming problem. Check to make sure that your solution is feasible! (c). Use TORA to find the optimal solution to the integer programming problem. Include a TORA screenshot of this optimal solution. (d). Is your answer in part (b) also an optimal solution to the integer programming problem? Explain.

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