Sycamore Basketball Company forecasts a 500-unit demand for its latest basketball hoop syste during the next quarter. This hoop is assembled from three major components: support pole, backboard and rim. Below are the production times and labour hours available. Note that each component produced must go through each department. Department Pole Backboard Rim 2.5 Time Available 2000 900 1500 0.5 1/5 1 The company also has the option of contracting the production of support poles or rims. The costs for manufacturing each component or purchasing each component are given in the table below. Purchase Cost Component Pole Backboard Rim Manufacturing Cost $60 $80 $30 $95 $45 a. How many of each component should they make and how many should they purchase? b. How many poles should be produced if each one costs $62.50 to manufacture? Explain why. Do not resolve the problem if you can determine the answer from a sensitivity analysis. If you cannot determine the answer from a sensitivity analysis, explain why and re-solve. c. From the original problem, if the cost of manufacturing poles changes to $70, how many poles should be produced? Explain why. Do not resolve the problem if you can determine the answer from a sensitivity analysis. If you cannot determine the answer from a sensitivity analysis, explain why and re-solve. d. Suppose that they have an opportunity to hire 100 additional hours for Department A. What is the most they would be willing to pay for each hour