Inferior Tile produces square vinyl floor tile is three sizes, small (8 X 8), medium (12X12) and large (16 X 16). The tile produced on three machines that vary in terms of the width of the tile produced. Machine 1 produces tile that is 12 inches wide, machine 2 produces tile that is 16 inches wide, and machine 3 produces tile that is 24 inches wide. The small tile can be produced on any one of the three machines, however there will be waste when Machine 1 is used. That is, the width of the tile will be 8 inches, leaving 4 inches of waste. There will be no waste on the other to machines since 2 smalls (8 X 8) produced on machine 2 will 16 inches wide and three tiles produced on machine 3 will be 24 inches wide. The same logic applies to medium and large tiles. The forecasted demand for the following production period is to produce 9,600 small, 11,200 medium and 4,200 large tile squares. The machines have a limited capacity and the time required in minutes to cut each tile varies on the machine as shown in the table below.

*An 8X16 inch tile from machine 3 cannot be cut in half and is considered 8 inch waste.

Time in minutes (machine 3 can cut three 8 X 8 tiles in 30 seconds).

Machine 1 Machine 2 Machine 3

Small .2 .4 .5

Medium .3 .3 .6

Large N/A .4 .5

Time available 35 hrs 35 hrs 40 hrs

Formulate the LP model to determine how many tiles should be cut on each machine and meet the forecasted demand and minimize waste.