1. The problem is to find the optimal values of variables $P$, $B$, $H$, and slack variables in an optimization context, typically linear programming. 2. The general approach uses the objective function to maximize or minimize, subject to constraints expressed as inequalities. 3. Slack variables are added to convert inequalities into equalities, allowing the use of methods like the Simplex algorithm. 4. For each constraint of the form $Ax + By + Cz \leq D$, add a slack variable $S \geq 0$ to get $Ax + By + Cz + S = D$. 5. Set up the initial Simplex tableau including $P$, $B$, $H$, slack variables, and the objective function. 6. Perform pivot operations to improve the objective value step-by-step, choosing entering and leaving variables based on the tableau. 7. Continue iterations until no further improvement is possible, indicating optimal values. 8. The final values of $P$, $B$, $H$, and slack variables are read from the tableau, where slack variables indicate unused resources. 9. This method ensures all constraints are satisfied and the objective function is optimized.