Which boundary type is drawn for the inequality y < 2x + 1 and why?

Graph the inequality y ≥ -3x + 2. Using the test point (0,0), determine which side should be shaded.

Put the inequality 2x + 5y ≤ 10 into slope-intercept form, identify the y-intercept and slope, and state whether the boundary is solid or dashed.

A conference event has seating constraints. Room A can seat 3 per table and Room B can seat 5 per table. They must seat at least 100 total people and have at most 30 tables combined. Let a = the tables in Room A, and b = the tables in Room B. Form the system of inequalities and determine one feasible integer solution, $(a,b)$, that will meet both constraints. Show your work.

A company makes two products: $A$ and $B$. Each product $A$ gives \(30 in profit and uses 2 hours of labor; each product $B$ gives \)50 in profit and uses 3 hours of labor. The weekly labor available is at most 60 hours per week. They must make at least 5 units of product $A$. There is no minimum for $B$. Set up a system of inequalities and determine which corner of the feasible region (integer or fractional that is allowed) that will maximizes the profit: $P=30A+50B$. Show all calculations.