MM&M Canada Ltd is a new startup company that is trying to capture part of the demand for electric bicycles in the Lower Mainland. The company has a small assembly office located in Kitsilano, where all models are assembled, tested and packaged. The company has recently launched two new models: Max123 and Min456. The suggested retail price is $1750 for the Max123 and $1980 for Min456. It takes three labourhours to assemble each Max123. In addition, 2.5 hours is required in the testing department and 1 hour is required in the packaging department for each Max123 produced. Each Min456 requires 2 hours of assembly, 1.25 hours in testing and 1.3 hours in packaging. For the next month, the manager can dedicate up to 900 labourhours for assembly, up to 500 labourhours for testing and up to 400 labourhours for packaging. The hourly labour costs are $35 per hour for assembly time, $32.50 per hour for testing time and $20 per hour for packaging. The costs for the parts used for assembly are $450 and $570 for Max123 and Min456, respectively. The number of already committed and anticipated orders far exceeds management's forecast for both models. Management has met with its salespeople and they have decided that at least 45% of the total production must be allocated to the Min456 models. Furthermore, they have decided that no more than 120 Max123 bikes should be produced and at least 50 Min456 models should be produced in their first production month. Answer the following: 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 prot. Solve using graphical methods ONLY as shown in class using ONLY lsoprofit lines (level curves) (do not solve by evaluating all the extreme corners of the feasible area). Make sure to plot the Max123 model along the horizontal axis of your graph paper. Clearly state the optimal solution in terms of the business problem. Be sure to state the maximum prot of the optimal solution. b) Using your answer in part a) solve algebraically for the constraints involved in the optimal solution. c) Using your optimal solution, calculate the amount of slacklsurplus available for all resources defined as operational constraints. d) Suppose the company can buy additional testing time at a favourable cost. Should it do so? State why or why not. How much more should they consider buying if they do purchase additional testing time at a favourable cost? (assuming they don't want to buy any additional resources other than testing) e) Suppose the company can buy additional assembly time at a favourable cost. Should it do so? State why or why not. How much more should they consider buying it they do purchase additional assembly time at a favourable cost? (assuming they don't want to buy any additional resources other than assembly)