Solving the linear programming problems

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1) The linear program Max 3X1 + 2X2 is solved subject to the constraints i) X1 + X2 =<10 ii) 3X1 + X2 =< 24 iii) X1 + 2X2 =< 16 and iv) non-negativity for both X1 and X2. Which of the following statements is true?

A.The optimal solution occurs at (4, 6).
B.The optimal solution value is 27.
C.The optimal solution occurs at (8, 0) and the optimal value is 24.
D.The optimal solution occurs at the point (6, 6).

2) The linear program Max 3X1 + 2X2 is solved subject to the constraints i) X1 + X2 =< 10 ii) 3X1 + X2 =< 24 iii) X1 + 2X2 =< 16 and iv) non-negativity for both X1 and X2. After solving the linear program, the objective function coefficient for X1 is changed from 3 to 5. Now the linear program is re-solved. Which of the following statements is true?

A.The new optimal solution occurs at (4, 6).
B.The new optimal solution occurs at (8, 0) and the optimal value is 30.
C.The new optimal solution occurs at the point (6, 6).
D.The new optimal solution value is 41.

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