### LEGO MY SIMPLEX (Pendegraft, Norman, Lego My Simplex, OR/MS Today, February 1997)

This activity is an adaptation of Norman Pendegraft's exercise described in OR MS Today . Most students get some exposure to Linear Programming and the Simplex Method in a quantitative methods course. Most OPM textbooks provide a recap of the theory as an appendix. The exercise LEGO MY SIMPLEX quickly and simply reintroduces linear programming theory in the context of production and resource allocation. Students are divided in small groups and are asked to build tables and chairs using Lego parts. This is followed by a discussion of the optimal solution, sensitivity analysis and the limitations of Linear Programming.

Groups of students (usually no more than 4) receive a bag containing LEGO pieces for parts and index cards for labor hours, and are asked to produce tables and chairs (see Figure 1) with a goal to optimize profit. In the version we play, we introduced two varieties: The COMMERCIAL (bright colors) and MILITARY (camouflage) with different selling prices but identical resources.

Figure 1. Product Mix

 Table Chair

 Students are asked to place the tables and chairs on the corresponding number of index cards. The solutions are different for the two varieties. The game can then extend to cover sensitivity analysis by asking students what an additional LEGO part is worth. The game information is given below. This exercise is ingenious in its simplicity. Students get a real grasp on shadow prices and what they really measure given the unit cost of resources. The demonstration takes about 20 to 30 minutes and can be easily extended to include other elements. LEGO MY SIMPLEX game information:

 Product: Tables and Chairs Client: Commercial (bright color) Military (camouflage) Raw Material: large blocks -- total available 6 small blocks -- total available 8 Labor: 3 hours per table 2 hours per chair there are 11 labor hours available (white index cards)

 Selling Price: Public Military Table \$57 \$61 Chair \$37 \$41

 Objective: Maximize Profit Costs: large blocks -- cost per block \$8 small blocks -- cost per block \$5 each labor hour costs \$8