Blog Post

# A Real Life Optimization Problem

I am part of a team at my college working on getting new storage closets installed for my department. The options are for closets that are 30″, 36″, or 42″ wide. The closets are 18 ¾” deep, and 63 ½” in height.

In one room, the space in which the closets are to be installed is 54 ¾” x 97 ½” x 96″. In another room, the space is 54 ¾” x 114″ x 96″. However, in the second room, there is a whiteboard rail that is 3 ¼” wide that protrudes into the space.

There are also plans to store 48″ x 36″ tri-fold poster boards in closets that are 24″ x 36″ when folded. There also needs to be enough clearance for the closet doors to open.

At a meeting I attended the other day, I was asked, “How many 30″, 36″, and 42″ closest should we order to maximize the amount of storage space, while taking into account the size of the items being stored?”

We settled on two 30″ wide closet and one 36″ wide closest in each room. This means that 96″ of the available 97 ½” wall space will be used in one room, and 96″ of the possible 114″ will be used in the other room, not taking into account the whiteboard rail or the clearance for the closet doors to open.

What would you decide in this case? What would you order to optimize the space being used in this case?

##### By Jon Oaks

College Math Instructor. Tech Enthusiast. Visionary. Creative Genius. But above all, I enjoy what I do. That is why I am a teacher. Because I like to teach.