It is known that the garment factory has 70 meters of cloth and 52 meters of cloth. It is planned to produce 80 sets of M and N garments with these two fabrics. It is known that it takes 1. 1 meter cloth and 0.4 meter cloth to make a set of n clothes, which can be profitable. 50 yuan, it takes 0.6m for A cloth and 0.6m for B cloth to make a set of n clothes.

Solution: If M model X sets are produced, N model 80-x sets are produced.

1. 1x+0.6(80-x)≤70( 1)

0.4x+0.9(80-x)≤52(2)

By (1)

1. 1x+48-0.6x≤70

0.5x≤22

x≤44

By (2)

0.4x+72-0.9x≤52

0.5x≥20

x≥40

therefore

40≤x≤44

Profit y = 50x+45 (80-x) = 50x+3600-45x = 3600-5x.

For this linear function, the smaller x is, the larger y is.

When x=40

The maximum profit Y=3600-5×40=3600-200=3400 yuan.