Questions: 25x + 175y

Solution Steps

To determine the most money Donnie can raise in a month, we need to formulate the objective function based on the given information. The objective function represents the total amount of money raised, which is a function of the number of church groups (x) and lunch locals (y). The objective function can be expressed as:

Objective Function: \( Z = 25x + 175y \)

This function needs to be maximized given the constraints on the number of hours available for writing each month.

The objective function to maximize the total amount of money raised is given by:

\[ Z = 25x + 175y \]

where \( x \) is the number of church groups and \( y \) is the number of lunch locals.

The constraint based on the maximum hours available for writing is:

\[ x + y \leq 12 \]

Additionally, we have the non-negativity constraints:

\[ x \geq 0, \quad y \geq 0 \]

By solving the linear programming problem with the objective function and constraints, we find the optimal values for \( x \) and \( y \). The optimal solution yields:

\[ x = 0, \quad y = 12 \]

Substituting the optimal values into the objective function:

\[ Z = 25(0) + 175(12) = 2100 \]

Final Answer