A pet daycare facility offers pet sitting services where owners can drop off their pets for training and socializing with other pets. To feed the pets, the daycare makes two types of pet food. A bag of freeze-dried nuggets costs $7.99 and contains 21 units of proteins, 4 units of fiber, and 15 units of fat. A bag of dehydrated food costs $11.26 and contains 28 units of protein, 7 units of fiber, and 20 units of fat. The minimum daily requirements are usually 300 units of protein, 75 units of fiber, and 220 units of fat. Formulate the information as an LP problem and answer the following questions.

a. How many bags of freeze-dried nuggets and dehydrated food should the facility make each day to minimize the total cost? What is the lowest cost?

b. Identify binding and nonbinding constraints and report the surplus value as applicable.

c. There are usually more pets being dropped off during holidays, and the minimum daily requirements increase to 500 units of protein, 100 units of fiber, and 330 units of fat. How many bags of freeze-dried nuggets and dehydrated food should the facility make each day during the holidays? What is the lowest cost in this scenario?