Solve each for y

Graphing Inequalities

Do you know “Half-Plane”?

Boundary--A line or curve that separates a graph into two parts.Half-Plane--The region of a graph on one side of a boundary that contains the solution set of an inequality.

Stress:“>>” Means upper half-plane excluding the boundary

“≥≥” Means upper half-plane including the boundary

“<<” Means lower half-plane excluding the boundary

“≤≤” Means lower half-plane including the boundary

PS. When the boundary is excluded, the boundary line should be dashed.

Graph then find the solutions of the inequalities.

Graph then find the solutions of the inequalities.

(10 minutes)

Cal Clueless spent less than four hours doing math and English homework last night. He spent more time working on math than on English. Cal spent at least a half-hour working on English. Restate the constraints algebraically in terms of x (math) hours and y (English) hours.

Cal Clueless spent four hours doing math and English homework last night. He spent more time working on math than on English. Cal spent at least a half-hour working on English. Restate the constraints algebraically in terms of x (math) hours and y (English) hours.

Graph these inequalities on your calculator. What do you see?

Cal Clueless studies mathematics it boosts his grade point average (GPA) by 0.001 per hour. Every hour that he studies English his GPA boosts by 0.0011 per hour.

Can you write this GPA boost as an equation.

Cal Clueless studies mathematics it boosts his grade point average (GPA) by 0.001 per hour. Every hour that he studies English his GPA boosts by 0.0011 per hour.

Can you write this GPA boost as an equation.

How Cal can maximize his GPA with the above constraints?

Clarence’s Carpentry Shop makes tables and chairs. Each table requires 5hr of woodworking and 4 hours of finishing. Each chair requires 10hrs of woodworking and 3hr of finishing. Each month Clarence has 600hr of labor available for woodworking and 240hr for finishing. The profit on each table is $60 and $48 on each chair. How many of each product should be made each month in order to maximize profit?

let x = The number of tableslet y = The number of chairs