CCSS IP Math I 1.4.1 Example 3

A school supply company produces wooden rulers and plastic rulers. The rulers must first be made, and then painted.
  • It takes 20 minutes to make a wooden ruler. It takes 15 minutes to make a plastic ruler. There is a maximum amount of 480 minutes per day set aside for making rulers.
  • It takes 5 minutes to paint a wooden ruler. It takes 2 minutes to paint a plastic ruler. There is a maximum amount of 180 minutes per day set aside for painting rulers.
Write a system of inequalities that models the making and then painting of wooden and plastic rulers.
  1. Identify the information you know.
  2. Write an inequality to represent the amount of time needed to make the rulers. Let w represent the wooden rulers and p represent the plastic rulers.
  3. Write an inequality to represent the amount of time needed to paint the rulers. Use the same variables to represent wooden and plastic rulers.
  4. Now consider the constraints on this situation. It is not possible to produce a negative amount of either wooden rulers or plastic rulers; therefore, you need to limit the values of w and p to values that are greater than or equal to 0.
  5. Combine all the inequalities related to the situation and list them in a brace, {. These are the constraints of your scenario.