<p> Project AMP Dr. Antonio Quesada – Director, Project AMP</p><p>MAXIMIZING CARTONS PER PALLET</p><p>GOAL: Maximize the number of tennis ball cylinders packed in cartons per shipping carton.</p><p>PROBLEM SITUATION:</p><p>You are the packaging engineer for Spaulding Company producing top quality tennis balls. Your task is to calculate the maximum number of tennis ball cartons per pallet for finished good storage and distribution to Wal-Mart. The following parameters will guide your decision-making:  Only standard tennis balls are packaged.  3 tennis balls per cylinder canister  24 canisters per shipping carton  Maximum cube size of pallet is 40" x 48" x 54"  Cartons will all have the same orientation (i.e., the position of the carton tape) on the pallet</p><p>1. Using the string and a ruler, measure "perimeter" of tennis ball. Circumference = ______in.</p><p>2. Calculate the radius of the tennis ball. Radius = ______in.</p><p>3. Calculate the volume of the cylinder canister. Volume = ______in3</p><p>4. Calculate the volume of the shipping carton. Volume = ______in3</p><p>5. What combinations of carton dimensions are possible given 24 canisters per shipping carton?</p><p>Cylinders/ layer 1 2 Layers / carton 24 12 Project AMP Dr. Antonio Quesada – Director, Project AMP</p><p>6. Prepare a table using the List function on your graphing calculator. Use the above table to calculate the length and width measurements of the carton possibilities. Use the following equations to compute the values:</p><p>L1 L2 L3 L4 L5 Length Width Height Carton Cartons per Dia * (# of Dia * (# of Volume / (L1 * L2) layers per pallet cylinders) cylinders) pallet iPart (48/L1) * iPart (54 / L3) iPart (40/L2) * L4</p><p>7. What are some limitations of this model?</p><p>8. How can this problem be solved by graphical or algebraic means?</p><p>9. How can you generalize this optimization process if the product changes (e.g., golf balls, Kleenex boxes, cans of soup, pyramid paperweights, etc.)?</p>