Zippy motorcycle manufacturing produces two popular pocket bikes (miniature motorcycles with 49cc engines): the Razor and the Zoomer. In the coming week, the manufacturer wants to produce a total of up to 700 bikes and wants to ensure that the number of Razors produced does not exceed the number of Zoomers by more than 300. Each Razor produced and sold results in a profit of $70, and each Zoomer results in a profit of $40. The bikes are identical mechanically and differ only in the appearance of the polymer-based trim around the fuel tank and seat. Each Razor's trim requires 2 pound of polymer and 3 hours of production time, and each Zoomer requires 1 pound of polymer and 4 hours of production time. Assume that 900 pounds of polymer and 2400 hours are available for production of these items in the coming week.
Here are the 3 questions:
1. Formulate an LP model for this problem. (Clearly define all the decision variables; Formulate the objective function and all the constraints)?
2. Sketch all the constraints and the feasible region for this problem in a coordinate system?
3. Determine the optimal solution and its resulting optimal profit?