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. let’s define the decision variables as follows: r: the number of razors to make; z: the number of zoomers to make 1. formulate the objective function of this farmer. 2. write down all the constraints of this lp problem. 3. create a coordinate plane, putting r on the horizontal axis and z on the vertical axis. 4. plot all boundary lines. 5. identify feasible region. 6. compute the coordinates and the objective value for each corner of the feasible region. 7. clearly state your optimal solution and optimal objective value. g