Electrocomp$$s management in Problem $7\mathrm{.}14$ above, realizes that it forgot to include two critical constraints. Management decides that there should be a minimum number of air conditioners produced to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced. a$.$ If Electrocomp decides that at least $20$ air conditioners should be produced but no more than $80$ fans should be produced, what would be the optimal solution? How much slack or surplus is there for each of the four constraints? b$.$ If Electrocomp decides that at least $30$ air conditioners should be produced but no more than $50$ fans should be produced, what would be the optimal solution? How much slack or surplus is there for each of the four constraints at the optimal solution?