solve this question

2(a) Hannah Shaw nds that one component of a system's cost is the cost of system failure. Failure costs can be reduced by designing a more reliable system. A simplied expression for system lifecycle cost, 0, can be written as a function of the system's failure rate: O=%+CRX/\\Xt Here, 0; is investment cost ($ per hour per failure), GR is the system repair cost, /\\ is the system failure rate (failures per operating hour), and t is the operating hours. i. Assume that 0;, CR, and t are constants. Derive an expression for A, say A', that optimizes C. [5 points] ii. Does the equation in part (i) correspond to a maximum or minimum value of C? Show all work to support your answer. [3 points] ii. What tradeoff is being made in this problem? Clearly explain your reasoning. [2 points]