Formulate a linear programming model in Excel and output $(1)$ activity start times that minimize the project's duration given a particular budget $(2)$ activity start times that minimize the project's cost given a particular project duration. Project information is showed in the table below. Times are in weeks. Costs are in $$10,000.$

Please create a LP model to answer the following questions.

$($a$)$ If there is a budget of $$850,000$ for the banquet, how quickly can the project be finished?

$($b$)$ If the project has already been advertised for a date $14$ weeks from now, how

inexpensively can the project be completed?