As part of an aerospace product, two sheets of aluminium need to be joined. Riveting and friction stir welding are both joining technologies, and both technologies are certified to join sheet aluminium for this application. A riveting tool costs 8000 to purchase. Because it is a very operator-intensive process and requires large amounts of consumables, each 1 m of joint costs 420. Purchase and commissioning of a friction stir welder costs 42000. Each joint is almost automated, and there are very few consumables, therefore each 1 m of joint costs 210. a. For each joining technology, write a formula to calculate the total cost for a given length of joining. (2 marks) b. Initial orders amount to a total of 102 m of joining. Using the formulas generated in part a, show which joining technology is the most cost effective for this first batch of orders. (4 marks) c. Produce a graph that can be used to determine under which conditions each of the joining technologies is the most cost effective. Use this graph to justify the minimum length of joining needed to make buying a friction stir welder cost effective. Explain how this graph was used to make this decision on which technology is the most cost effective. (8 marks) 2 marks are allocated for producing a graph that correctly shows the information requested and 2 marks are allocated for using good mathematical style in your graph. The remaining marks are allocated to your explanation.