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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: Read the problem. It may be helpful to underline important info! Step 2: Define Variables. (Look at the question in the last sentence to help you.) Let x = # of plain chairs. Now you define y: y= Step 3: Find the Objective Quantity. (This is what you are trying to maximize/minimize.) Step 4: 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.

          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: Read the problem. It may be helpful to underline important info! Step
2: Define Variables. (Look at the question in the last sentence to help you.)
Let x = # of plain chairs. Now you define y:
y=
Step 3: Find the Objective Quantity. (This is what you are trying to maximize/minimize.)

Step 4: 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.

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 is65, how many rocking chairs of each type should the company make per day to maximize profits AND what is the maximum profit?

Step 1: Read the problem. It may be helpful to underline important info! Step
2: Define Variables. (Look at the question in the last sentence to help you.)
Let x = # of plain chairs. Now you define y:
y=
Step 3: Find the Objective Quantity. (This is what you are trying to maximize/minimize.)

Step 4: 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.

Added by William C.

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