$($C$)$ The two plants described above $($a$)$ and $($b$)$ are now owned by the same parent company, which is trying to maximize the combined net profit of both plants. The parent company has relaxed the restrictions on monomer supply to each plant $(75$ tons$/$hr and $45$ tons$/$h for the second plant$).$Instead, the parent company can provide a combined monomer supply to both plants of $120$ tons$/$hr at most. Therefore, it is necessary to distribute the available monomer between the two plants optimally. What are the optimal production capacities of polymers A and B in each plant that will maximize the combined net profit of both plants?Comment on the results of $($a$),($b$),$ and $($c$)$