(Solved): Consider the following linear programming model of fit:   The optimal ...

Consider the following linear programming model of fit:

 

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The optimal simplex table is the following:

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a. What is the new solution if resource one increases by 20 units.
b. What is the new solution if the profit of product 2 increases by 3 units.
c. Delete the variable X1.
d. Add the constraint 2X1 + 3X2 <= 6

\( \begin{array}{ccl}\text { MAX } & Z=3 X 1+2 X 2 & \text { PROFITS } \\ \text { Sa. } & 4 X 1+3 X 2 \leq 12 & \text { (RESOURCE 1) } \\ & 4 X 1+X 2 \leq 8 & \text { (RESOURCE 2) } \\ & 4 X 1-X 2 \leq 8 & \text { (RESOURCE 3) } \\ & X j \geq 0 & \end{array} \) \begin{tabular}{|l|c|c|c|c|c|c|} \hline V. BASIC & X1 & X2 & H1 & H2 & H3 & Id \\ \hline X2 & 0 & 1 & \( 1 / 2 \) & \( -1 / 2 \) & 0 & 2 \\ X1 & 1 & 0 & \( -1 / 8 \) & \( 3 / 8 \) & 0 & \( 3 / 2 \) \\ H3 & 0 & 0 & 1 & \( -2 \) & 1 & 4 \\ \hline\( - \) Z & 0 & 0 & \( -5 / 8 \) & \( -1 / 8 \) & 0 & \( -17 / 2 \) \\ \hline \end{tabular}