Assigning Tasks

A data processing department wishes to assign five programmers to five programming tasks $($one programmer to each task$).$ Management has estimated the total number of days each programmer would take if assigned to the different jobs, and these estimates are summarized in the Excel file HW$4$ under the Assigning Tasks Tab.

Hint: Maybe the decisions of allocating programmers to task a binary variable. If a programmer is attached to a task, the corresponding variable is $1,$ otherwise, $0.$ Make sure you include the constraints to ensure we have one programmer to each task.

Determine the assignment that minimizes the total programmer days required to complete all five jobs.

$\backslash$table$[[$Task$,$Program$],[1,],[2,1],[3,],[4,],[5,]]$

How would the solution change if programmer $3$ could not be assigned to tasks $2$ or $4?$

$\backslash$table$[[$Task$,$Programmer,$],[1,,],[2,1,],[3,,],[4,,],[5,,]]$