Fast food companies know that if they sell a certain product for a lower cost they will sell more of that product. However, if they sell the product for too low of a cost they lose money even though they are selling more. At Frank's Hamburger Barn, they discovered that if they price their hamburger at $3.25 each, they will sell 30,000 hamburgers in a month. However, they found that if they want to sell 50,000 hamburgers in a month, they need to sell them for $2.55 each. The owners of Frank's also discovered that in order to make a profit they need to sell the hamburgers for at least $2.15

a. What quantity represents the input in this situation? Define a variable to represent this quantity.

b. What quantity represents the output in this situation? Define a variable to represent this quantity.

c. Without using regression, determine a formula for the linear function, , that represents the given situation.

d. Determine a practical domain for the function . e. Determine a practical range for the function .