$(1)$ Please solve the following problem using linear programming method. Please send your

excel sheet with the optimal solution. Also, based on the sensitivity report, provide any two

managerial takeaways $($write these points within the excel sheet itself$).$

FreeFlight Tours is planning a charter trip to a major resort in Hawaii. The eight$-$day$-$seven$-$

night package will include round$-$trip air transportation, surface transportation, hotel, meals, and

selected tour options. The charter trip is restricted to $200$ persons, and past experience indicates

that there will be no problem finding $200$ participants. What the company must do is determine

the number of deluxe, standard, and economy tour packages to offer in this charter. These three

plans each differ according to seating and service for the air flight, quality of accommodations,

meal plans, and tour options. The table below summarizes proposed prices for the three packages

and corresponding expenses for FreeFlight Tours. The company has chartered a jet airliner for a

flat fee of $$20,000.$

In planning the trip, certain considerations must be taken into account:

At least $10\%$ of the packages must be of the deluxe type.

At least $35\%$ but no more than $70\%$ of the packages must be of the standard type.

At least $30\%$ must of the economy type.

The airliner allows for no more than $60$ deluxe packages.

The hotel requests a guarantee that at least $120$ of the tourists be on deluxe or standard

packages.

FreeFlight Tours wishes to determine the number of packages of each type to offer so as to

maximize total profit.