Geordie's Caf e bundles together pastry and drink items in the following way:

Combo 1: One cookie, one muffin, and one coffee. Combo 2: One muffin, one scone, and one coffee. Combo 3: Three cookies, three donuts, and three coffees. Combo 4: One cookie, one muffin, one donut, one scone, and one coffee. Combo 5: Two cookies, three muffins, one scone, and three coffees.

Organizers of a conference need to purchase 580 cookies, 600 muffins, 180 donuts, 200 scones, and 750 coffees for breakfast. Model this scenario as a linear system if the organizers can only purchase bundles from Geordie's Caf e and not individual items.

Find all solutions to your model from part (i), then explicitly give two realistic solutions. A realistic solution is a solution consisting of nonnegative integers.

Suppose that Geordie hires you as a consultant and asks you replace Combo 5 with a new Combo consisting of the same items (cookies, muffins, and so on), so that the organizers now have only one unique way of purchasing Combos to meet their requirements. Come up with such a Combo and show that it satisfies Geordie's condition. Your combo does not need to include every item, and can include as many or as few items of each item as you wish (though you may not use negative items).