Articulate and answer an integer programming model for this problem.
The Skimmer Boat Company manufactures three types of moulded fiberglass recreational boats--a bass fishing boat, a sik boat and a speedboat. The profit for a bass boat is $20,500, the profit for a ski boat is $12,000 plus the profit for a speedboat is $22,300. The company trusts it will sell more bass boats than the other two boats combined but no more than twice as many. The ski boat is its standard production model as well as bass boats and speedboats are modifications. The company has production volume to manufacture 210 standard (ski-type) boats- but a bass boat requires 1.3 times the standard production capacity as well as a speedboat requires 1.5 times the normal production capacity.
In addition merely 160 of the high powered engines that are installed in the bass boats and 2 of those installed in the speedboats are available. The company desires to know how many boats of each type to produce to maximize profit. Formulate as well as solve an integer programming model for this problem.