Problem $2($One Cup Coffee Shop$)$

The One Cup Coffee House stocks three varieties of fine coffee beans: Sumatra, Kona and T $50$ pts$.)$ To maintain the quality of their coffee, the total number of bags produced by the Coffee Hazu. exceeds $100$ bags per week. The coffee beans are carefully dried produced by the Coffee House never $400$ hours and $600$ drying tables are available. coffee of each variety to stock this week so

$\backslash$table$[[$Variety$,$Drying $($tables$/$bag$),$Roasting $($hours$/$bag$),$Profit bag$)],[$Sumatra$,1,2,6],[$Kona$,6,5,11],[$Tarrazu$,3,4,9]]$

Write a linear program for the problem.

What is the optimal production mix among different coffee varieties and the profit associated with it$?$

What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety?

One Cup is considering increasing the weekly bags to $150.$ If it costs One Cup $$3\mathrm{.}00$ per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production.

Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup.

Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for $24$ hours$/$ week. It takes $10,15$ and $10$ minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.