ONLY the 3rd question

We consider an application with n different job (types), each of which consumes m different resources. We dene the m x n resource matrix R, with entry Rw- giving the amount of resource i that is needed to run one unit of job j, for i = 1, . . . ,m and j = 1,. . . ,n. (These numbers are typically positive.) The number (or amount) of each of the different jobs to be processed or run is given by the entries of the nvector 3:, which we refer to as the \"input\". (These entries are typically nonnegative integers, but they can be fractional if the jobs are divisible.) The entries of the m-vector 19 give the price per unit of each of the resources. Remark. One example is a data center, which runs many instances of each of n types of application programs. The resources include number of cores, amount of memory, disk, and network bandwidth. 1. Let y be the mvector whose entries give the total of each of the m resources needed to process the jobs given by :6. Express y in terms of R and m using matrix and vector notation. 2. Let c be an nvector whose entries gives the cost per unit for each job type. (This is the total cost of the resources required to run one unit of the job type.) Express 0 in terms of R and 13 using matrix and vector notation. 3. Assume that the entries of the vector x are only known up to an interval. Specically, H m i" H00 3 a, where the inequalities are componentwise, and i E R\" and a 6 IL are known. Find the largest possible value of My gum, where 3) is the vector corresponding to input vector CE. Express your answer in terms ofthe rows TE, 73 = 1,. . . ,m of R