A store sells two kinds of bicycles, model A and model B. The store buys them unassembled from a wholesaler. Two employees are responsible for assembling the bicycles, and they are permitted to work no more than 6 hours each week to do this job. Working together to assemble model A, employee 1 works 3/4 hour and employee 2 works 1/2 hour. Model B requires 1/2 hour's work by employee 1 as well as 1 hour's work by employee 2. There is a $110 profit on each model A sold and $96 on each model B. Because of the popularity of the sport, the store is able to sell as many bicycles as they decide to assemble. How many bicycles of each model should they assemble in order to get the maximum profit?
Please include all of the steps in the problem.