Please break down each step for the following question: SweetHarbor Artisan Bakery produces three types of premium pastries: Almond Croissants $($Pastry A$),$ Chocolate Danishes $($Pastry B$),$ and Raspberry Linzer Tarts $($Pastry C$).$ Each pastry requires time on two key production machines: the Mixer and the Oven. The time $($in minutes$)$ required per unit is as follows: Pastry A takes $6$ minutes on the Mixer and $4$ minutes on the Oven; Pastry B takes $4$ minutes on the Mixer and $5$ minutes on the Oven; and Pastry C takes $4$ minutes on the Mixer and $2$ minutes on the Oven. The Mixer is available for $120$ hours $(7200$ minutes$)$ per week, and the Oven is available for $110$ hours $(6600$ minutes$)$ per week. The bakery can sell up to $1000$ units each of Pastry A and B$,$ and up to $200$ units of Pastry C$.$ Additionally, due to a contract with a luxury hotel, the bakery must produce at least $600$ units of Pastry A each week. The profit contributions are $$8$ for Pastry A$,$ $$6$ for Pastry B$,$ and $$9$ for Pastry C$.$ Answer the following questions based on this scenario: $$ Formulate a linear programming model to maximize the bakery$$s weekly profit.$$ Solve the model and recommend the optimal number of units to produce for each pastry type.$$ What are the allowable ranges for the profit contributions of each pastry type? Interpret these ranges for management.$$ If additional machine time could be made available, which machine $($Mixer or Oven$)$ would provide more value, and how much extra profit could be earned per minute added?$$ A boutique store offers to buy more than $200$ units of Pastry C if the price is reduced by $$4$ per unit. Should the bakery accept this offer? Justify your answer using sensitivity analysis.