PLEASE PRIORITIZE ANSWERING PARTS C) AND D)!

Potato-Potato Cycles manufactures and sells motorcycles in a variety of engines and configurations. The company has recently launched two new models: R30 and R40. The suggested retail price is $21,000 for R30 and $36,000 for R40. Note that because construction of cycles is continuous, portions of bikes can be constructed each month (solution not limited to integers).

It takes 9 labour-hours to assemble each R30 plus 0.7 hours in the packaging department for the R30 model. Each R40 model requires 10 hours of assembly and 2.3 hours in packaging. For the next month, the plant manager can dedicate up to 1000 labour-hours for assembly and up to 190 labour-hours for packaging. The hourly labour costs are $40 per hour for assembly time and $20 per hour for packaging. The costs for the parts used for assembly are $5,700 for the R30 and $6,950 for the R40 model.

The number of already committed and anticipated orders far exceeds managements forecast for both models. Management has met with the marketing department and they have decided that at least 35% of the total production must be allocated to the R40 models. Furthermore, they have decided that at least 22 of the R40 models must be fabricated in their first production month.

a) Formulate the problem into proper LP format to determine the number of units of each model to make in the first production month in order to maximize the total contribution to profit. Solve using graphical methods ONLY as shown in class using ONLY Isoprofit lines (level curves) (do not solve by evaluating all the extreme corners of the feasible area). Make sure to plot the R30 models along the horizontal axis of your graph paper. Clearly identify on your graph the feasible area, the isoprofit line and your optimal point or marks will be lost! Clearly state the optimal solution in terms of the business problem including the value of the objective function.

b) Using your answer in part a) solve algebraically for the constraints involved in the optimal solution and state the final answer in the context of the business problem. I suggest you use the method of finding the intersecting point by solving one equation for x1, then substituting this into the other equation which you can now solve precisely for x2.

c) Suppose Potato-Potato can buy additional packaging time at the same rate. Should it do so? State why or why not. How much more should they consider buying if they do purchase additional packaging time at a favourable cost? (assuming they dont want buy any additional resources other than packaging)

d) Suppose Potato-Potato can buy additional assembly time at the same rate. Should it do so? State why or why not. How much more should they consider buying if they do purchase additional assembly time at a favourable cost? (assuming they dont buy any additional resources other than assembly)

e) Suppose the company realizes that the competition in the marketplace results in demand only being available at an MSRP of $13,000. for each R30 model (assume everything else remains the same) then using your new profit line, estimate the coordinates of a possible new optimal solution and clearly state the optimal profit available in this case.