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Reddy Mikks produces both interior and exterior paints from two raw materials, \( M 1 \) and \( M 2 \). The following table provides the basic data of the problem:
\begin{tabular}{lccc}
\hline & \multicolumn{2}{c}{ Tons of raw material per ton of } & \\
\cline { 2 - 3 } & Exterior paint & Interior paint & \begin{tabular}{c}
Maximum daily \\
availability (tons)
\end{tabular} \\
\hline Raw material, \( M 1 \) & 6 & 4 & 24 \\
Raw material, \( M 2 \) & 1 & 2 & 6 \\
\hline Profit per ton \( (\$ 1000) \) & 5 & 4 & \\
\hline
\end{tabular}
a. Reddy Mikks wants to determine the optimum product mix of interior and exterior paints that maximizes the total daily profit. Formulate an appropriate linear programming model.
b. Determine the optimum solution graphically.
c. Determine the optimum solution using Simplex method.
d. Determine the range for the ratio of the unit revenue of exterior paint to the unit revenue of interior paint.
e. If the revenue per ton of exterior paint remains constant at \( \$ 5000 \) per ton, determine the maximum unit revenue of interior paint that will keep the present optimum solution unchanged.
f. If for marketing reasons the unit revenue of interior paint must be reduced to \( \$ 3000 \), will the current optimum production mix change?
g. Write the Dual of the LP formulated in part a.
h. Find the optimum solution of the Dual from the optimal table of the Primal in part c.
i. Consider the optimal solution in part c. If the daily availabilities of raw materials M1 and M2 are increased to 35 and 10 tons, respectively, use post-optimal analysis to determine the new optimal solution.
j. Investigate the optimality of the Reddy Mikks solution (part c.) for the objective function: \( z=3 x_{1}+2 x_{2} \)
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6:32 PM
9/13/2024
