Compute the linear programming problems
Problem 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).
Problem 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.
I need help to compute the given linear programming problems and selects the suitable options.