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 up to 700 bikes and wants to ensure the number of Razors produced does not exceed the number of Zoomer by more than 300. Each Razor produced and sold results in a profit of $70 while each Zoomer results in a profit of $40. The bikes are identical mechanically and only differ in the appearance of the polymer-based trim around the fuel tank and seat. Each Razor’s trim requires 2 pounds of polymer and 3 hours of production time while each Zoomer requires 1 pound of polymer and 4 hours of production time. Assume that 900 pounds of polymer and 2,400 labor hours are available for production of these items in the coming week. a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. What is the optimal solution?