In this question, consider the Matrix Chain Multiplication problem that we discussed in class. First, understand what is being asked to minimize in the problem. (a) Give the optimization objective function that you will develop a name. (b) Write down the variables of your function in between parenthesis and define what your function represents as complete and concise as possible in only one sentence, as we did in class. (c) We can start writing the right-hand side of the formulation in a recursive manner. Now spend a considerable amount of time to imagine how would an optimal splitting would look like for a set of matrices. Consider the last choice you would do to obtain this imaginative optimal solution. Yes, you are right! You must choose where to split. As you can guess, each index k is a different scenario. In the first scenario, assume that the number of operations to perform is minimized if only you split from the first index (i.e. k=1 ). Then, if the last spit was at k=1, the right-hand side would be some function of the function you have written for the corresponding sub-problem. Write down the right-hand side for the first scenario. (d) Write down the right-hand side for k=2. As you can guess, you need to do this for all valid k 's. (e) Now you are ready to minimize the set of all functions produced by different scenarios. Write down the whole formulation which collects all the above right-hand side functions into one as a minimization function