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

Table 1. shows the expected demand for the dvd at different suggested donation levels, and they can act as a single-price monopolist if they choose to. thereceipts will be used to fund gstcg supplies for their data collection and conservation work. at the end of each sea turtle nesting season, any excess funds are donated by the gstcg to a local non-profit sea turtle research and rehabilitation facility. table 1 suggested anticipated total marginal profit donation per number of dvd revenue revenue dvd request requests $19.00 0 $15.00 2 $9.50 4 $7.75 10 $3.00 15 $0.00 20 a. complete table 1 by computing the total revenue, marginal revenue, and profit columns. b. the president wants the gstcg to provide videos to generate the most possible donations (total revenue). what price, if any, is the president of the gstcg favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. c. the education outreach committee wants the gstcg to provide videos to the highest possible number of people. what price, if any, is the educational outreach committee favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. d. the treasurer of the gstcg wants the dvd program to be as efficient as possible so that the marginal revenue equals marginal cost. what price, if any, is the treasurer favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. e. the fundraising committee wants the dvd program to generate as much profit in donations as possible. what price, if any, is the fundraising committee favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer.