Amazon Web Services (AWS) offers cloud computing services to individuals, companies, and governments. They operate a total of k servers to which they must assign n tasks over the next minute. It is known that the time to complete task i on server j is seconds. Also, the electricity cost to complete task i on server j is cents. For simplicity, suppose that tasks can be split amongst servers, e.g., a task can be completed 60% by one server and 40% by another server, in which case the costs and times will be incurred proportionally. Formulate a linear program for AWS so that all n tasks can be completed on the k servers within the next minute and at minimum electricity cost. Clearly define your decision variables and any indices/parameters that you use. Also, be sure to write out your objective function and constraints in words and in math.