Tracy and Sky are partners of a small business. They own a new bakery shop by the local lake. They bake 5 kinds of cakes daily for sale. These 5 products and their information can be found in the given table. Using Birthday Cake as an example from the table, it takes 3.5 pounds of flour, no mixed berries, 2 pounds of cream, 6 eggs, 55 ounces of oil, and 0.5 gallon of milk to make a Birthday Cake. It can then be sold and brings in $15 profit per cake. Tracy and Sky sell all of their baked cakes within the same day. Here are their daily ingredient supplies. They have 120 pounds of flour, 60 pounds of mixed berries, 50 pounds of cream, 216 eggs, 2000 ounces of oil, 55 gallons of milk available for each daily operation. Due to the spacious refrigeration requirement for the Wedding Cake, no more than 3 Wedding Cakes can be made each day. In order to satisfy the local residents' requests, at least 8 Birthday Cakes must be made daily. In order to encourage the local college students to purchase, Tracy and Sky decided that the number of Cup Cakes must be at least 5 times more than the number of Gourmet Cakes.

In addition to the profits generated from selling these 5 types of cakes, Tracy and Sky sell their unused mixed berries to the local night club daily. Tracy and Sky receive $3.55 as profit for each pound of unused mixed berries sold to the night club.

Construct a linear program for Tracy and Sky to help them find the daily production operation that can maximize their total daily profit. Clearly list the decision variables, objective function, and constraints. You do NOT need to solve the program.

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