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.