Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non$-$smoking, beachfront smoking, lagoon view non$-$smoking, and lagoon view smoking. In order to decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information.

After adjusting for expected occupancy, the average nightly revenue for a beachfront non$-$smoking room is $$175.$ The average nightly revenue for a lagoon view non$-$smoking room is $$130.$ Smokers will be charged an extra $$15.$

Construction costs vary. The cost estimate for a lagoon view room is $$12,000$ and for a beachfront room is $$15,000.$ Air purifying systems and additional smoke detectors and sprinklers ad $$3000$ to the cost of any smoking room. Evans Enterprises has raised $$6\mathrm{.}3$ million in construction guarantees for this portion of the building.

There will be at least $100$ but no more than $150$ beachfront rooms.

Design considerations require that the number of lagoon view rooms be at least $1\mathrm{.}5$ times the number of beachfront rooms, and no more than $2\mathrm{.}5$ times that number.

Industry trends recommend that the number of smoking rooms be no more than $50\%$ of the number of non$-$smoking rooms.

There should be at least $15$ rooms of each kind.

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