Problem: A furniture company makes two types of rocking chairs, a plain chair and a fancy chair. Each rocking chair must be assembled and then finished. The plain chair takes 4 hours to assemble and 4 hours to finish. The fancy chair takes 8 hours to assemble and 12 hours to finish. The company can provide at most 160 worker-hours of assembling and 180 worker-hours of finishing per day. If the profit on a plain chair is $40 and the profit on a fancy chair is $65, how many rocking chairs of each type should the company make per day to maximize profits AND what is the maximum profit? Step 1: Define Variables. (Look at the question in the last sentence to help you.) Let x = # of plain chairs. Now you define y: y=

Step 2: Find the Objective Quantity. (This is what you are trying to maximize/minimize.)

Step 3: Find constraints. We will set up 4 constraints (inequalities) below.

Constraint 1: Write an inequality that shows that our x-value is 0 or positive.

Constraint 2: Write an inequality that shows that our y-value is 0 or positive.

Constraint 3: Write a constraint for # of assembly hours. Constraint 4: Write a constraint for the # of finishing hours.

Step 4: Graph the inequalities and shade the feasible region (Region that overlaps with all 4)

Step 5: Find all corner points of your feasible region.

Step 6: Test all corner points in your objective quantity from step 3.

Step 7: Answer the question in a sentence: How many rocking chairs of each type should the company make per day to maximize profits AND what is the maximum profit?