Question1: LP graphical analysis (you are strongly advised to use graph paper as the clarity of details is required for full marks) This problem will require uploading PDF images of three hand drawn/written pages. The first page is the diagram of the problem including all of part a, the second and third are the answers to parts b - e: Whizz Cycles manufactures and sells electric cycles in a variety of engines and configurations. The company has recently launched two new models: W10 and W20. The suggested retail price is $21,500 for W10 and $36,500 for W20. Note that because construction of cycles is continuous, portions of bikes can be constructed each month (solution not limited to integers).

It takes 9.5 labour-hours to assemble each W10 plus 0.8 hours in the packaging department for the W10 model. Each W20 model requires 10.5 hours of assembly and 2.2 hours in packaging. For the next month, the plant manager can dedicate up to 1100 labour-hours for assembly and up to 195 labour-hours for packaging. The hourly labour costs are $42.50 per hour for assembly time and $17.50 per hour for packaging. The costs for the parts used for assembly are $5,800 for the W10 and $6,850 for the W20 model.

The number of already committed and anticipated orders far exceeds management's forecast for both models. Management has met with the marketing department, and they have decided that at least 25% of the total production must be W20 models. Furthermore, they have decided that at least 25 of the W20 models must be fabricated in their first production month. Hand in the following drawn/written work:

a) Formulate the problem into "proper LP format" to determine the number of units of each model to make in thefirst production month in order to maximize the total contribution to profit. Solve using graphical methodsONLY as shown in class using ONLY Isoprofit lines (do not solve by evaluating all the extreme corners of thefeasible area). Make sure to plot the W10 models along the horizontal axis of your graph paper. Clearlyidentify on your graph the feasible area, the isoprofit line and your optimal point or marks will be lost! Clearlystate the optimal solution in terms of the business problem including the value of the objective function. (2marks)

b) Using your answer in part a) solve algebraically for the constraints involved in the optimal solution and statethe final answer in the context of the business problem. I suggest you use the method of finding theintersecting point by solving one equation for x1, then substituting this into the other equation which you cannow solve precisely for x2.The website https://www.symbolab.com/solver/system-of-equations-calculator provides a convenienttool for performing the algebra required. (2 marks)

c) Suppose Whizz can buy additional packaging time at the same rate. Should it do so? State why or why not.(assuming they don't want buy any additional resources other than packaging) (2 marks)

d) Suppose Whizz can buy additional assembly time at the same rate. Should it do so? State why or why not.(assuming they don't buy any additional resources other than assembly) (2 marks)

e) Suppose the company realizes that the competition in the marketplace allows them to adjust pricing. Now theycan sell the W10 models at an MSRP of $31,500 but the W20s can only sell for an MSRP of $34,500. (assumeeverything else remains the same) then using your new isoprofit line, estimate the coordinates of a possiblenew optimal solution and clearly state the optimal profit available in this case. (2 marks)