Identifying Constraints

Each short scenario describes a business situation. For each scenario, please write a short paragraph explaining which constraint or constraints is/are present, and why.

1. A taxi company limits its drivers to one eight-hour shift per day, with one half-hour break for a meal. A taxi cannot carry more than three passengers, all in the back seat, and cannot combine stops; that is, all the passengers must be going to the same destination.
2. Acme Unlimited sells custom machine tools. The sales department must send each order to Engineering for approval. There are no exceptions to this rule, which creates delays.
3. An online university offers six-week terms, with three two-week modules per term. Each module is supposedly limited to one topic, or set of related topics. Faculty members find it difficult to create interesting courses, and students express frustration with their learning experiences.

Part II: Describing Constraints

For each situation, write down the appropriate constraint. Please use the standard symbols “+” and “-” for plus and minus, and “ * ” for multiplication; however, if you find the symbols “≤” and “≥” difficult to keep straight, you may write “LE” for “Less than or equal to,” and “GE” for “Greater than or equal to.”

Example: An office is buying filing cabinets. The Model A cabinet holds a maximum of 3 cubic feet of files. Model B holds a maximum of 4.5 cubic feet of files. At any time, the office will have a maximum of 17 cubic feet of files that need to be stored. (A bit more cabinet space wouldn’t be a problem, but not enough would be. The files can’t be stacked on the floor.) Write a constraint on the number of cabinets the office should acquire.

Variables:

A = number of Model A cabinets purchased

B = number of Model B cabinets purchased

Answer:

A*( 3 cubic feet) + B*(4.5 cubic feet) ≥ 17 cubic feet

Or

A*( 3 cubic feet) + B*(4.5 cubic feet) GE 17 cubic feet

1. Patty makes pottery in her home studio. She works a total of six hours (360 minutes) per day. It takes her 10 minutes to make a cup, 15 minutes to make a bowl, and 30 minutes to make a vase. Write a constraint governing the joint production of cups, bowls and vases in a day. (Trans: “joint” = determined together; each affected by the others.)

Variables:

C = number of cups made

B = number of bowls made

V = number of vases made

1. An aid agency is buying generators for storm survivors. The generators will be shipped on a convoy of flatbed trucks having a total usable cargo area of 1,350 square feet. Generator A has a footprint (floor space required) of 8 square feet, and Generator B has a footprint of 12 square feet. Write a constraint governing the number of generators of each type than can be shipped.

Variables: