Final answer:
The weekly cost C can be determined using the manager's estimate of $250 plus $1.25 per customer. The exact relationship between cost and price cannot be determined without the demand equation. The function for weekly profit cannot be determined without information about revenue and cost.
Step-by-step explanation:
To determine the weekly cost C as a function of the number of patrons q, we can use the manager's estimate that weekly expenses are $250 plus $1.25 per customer. This can be represented by the equation C = 250 + 1.25q, where C is the weekly cost and q is the number of patrons.
To combine this with the demand equation and state the weekly cost C as a function of the hourly price P, we need more information about the demand equation. Without that information, we cannot determine the specific relationship between cost and price.
To determine the weekly profit as a function of p, we would need additional information about the revenue and cost associated with the company's operations. Without that information, we cannot provide a specific function for weekly profit.