4. Inferior Tile produces square vinyl floor tile is three sizes, small (8 X 8),

Question

4. 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 48,000 small, 84000 medium and 54000 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.

Time in minutes per one square tile.

Machine 1       Machine 2       Machine 3

Small                           .2                     .4                     .5

Medium                       .3                     .3                     .6

Large                           N/A                 .4                     .5

Time available             200 hrs 350 hrs 400 hrs

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

.

4a. How many small tiles should be produced on each of the three machines?

4b. What would be the total waste if 85,000 medium sized tile were required?

c. What would be the total waste if machine 2 was available 355 hours per week?

Explanation / Answer

To produce 48000 small tiles we use machine no 1 which takes 0.2 minutes for a tile i.e.each 12 seconds it cuts one small tile i.e.300 tiles per hour. As machine 1 is aailable for 200 hours it can produce 200*300=60000tiles much ahead of the demand so it will have 40 hours for medium tiles

similarly machine 2 can produce 200*350=70000 tiles without wastage leain a shortfall of 14000 medium tiles

so machine 3 has to produce 14000 small and 54000 lare tiles.

54000 large tiles will take 54000*0.5/60=450 hours

as it is aailable for only 400 hours we can produce only 400*0.5*60=48000 large tiles

machine one can produce medium tiles so all 85000 medium tiles hae to be produced on machine 1,2&&3

machine 2 can produce only 70000 so balance 14000 will hae to be produced om mahine 1 without wastage.

machine one can produce200*240=48000 medium tiles balance37000will be produced on machine 2&3

machine 2 can produce 37000 tile resultin in wastage of 37000*4= 148000 inchesof material

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