Question $2.$ Integer Programming Modeling $(7$ points$)($Excel implementation not needed$)$Northeastern Airlines $($NEA$)$ is considering expanding its operation in which it will purchase new aircraft for its European routes. NEA is looking at the purchase of Boeing B$797$s and Airbus A$450.$ The budget allocated for new plane purchases is $$800$ million. Boeing B$797$s cost $$40$ million per plane and Airbus A$450$s cost $$30$ million each.NEA has allocated another budget of $$10$ million for the additional personnel hires to support the operation of the new planes. Each B$797$ requires $$400,000$ in new personnel hires and each A$450$ requires $$350,000.$ On average, each of these planes are expected to generate an annual profit of $$3\mathrm{.}5$ million and $$2\mathrm{.}7$ million respectively $($net of plane cost, personnel cost, maintenance cost, fuel cost, etc.$).$In an effort to achieve some uniformity with respect to fleet appearance, spare parts and maintenance procedures, NEA executives have specified that they will not buy fewer than $10$ airplanes of any type if they buy it $($but they don't have to buy both types of planes$).$ Their objective is to maximize total annual profit.Currently, the available maintenance facilities allow $600$ days of maintenance per year for newly purchased planes. Each B$797$ requires $45$ days of annual maintenance and each A$450$ requires $35$ days. However, it is possible to increase the available maintenance time to $900$ days. To accomplish this, the maintenance facilities would have to be expanded at a cost of $$16$ million, which will come out of the budget for new plane purchase.In addition, the expansion would increase operating costs by $$18$ million annually, an expense that would reduce annual profit$\mathrm{.}2\mathrm{.}1$ Writing below in plain words, what are the decisions that NEA is trying make and what is the objective that NA wants to achieve? $(2$ points$)$