2. Nice Wheels manufactures road bikes and mountain bikes. Management wants to determine the number of each type of bike to produce that will maximize profit over the next six- week planning horizon. Constraints affecting production quantities are due to the production capacities in three departments: welding, assembly, and testing. For the six- week planning period, 275 hours of welding time, 325 hours of assembly time, and 300 hours of testing time are available. The time required to manufacture the two types of bicycles is shown in the following table: Welding Assembly Testing Labor Hours Road Bike Mountain Bike 5.5 4 3.5 3 2 Road bikes provide a profit of $72.25 per bike and mountain bikes provide a profit of $67.75 per bike. Formulate a linear optimization model that will maximize profit for Nice Wheels satisfying all constraints. (You do not need to find the optimal solution).