52. Correct. The answer is true. The expressions with Z in them in the first 4 equation tell us how much inputs are required to clean up. In the last equation the amount of pollution is 0.03X1. Setting Z equal to 0.9 times the amount of pollution requires cleaning up 90% of pollution.

X1 = 0.10X1 + 0.12X2 + 0.15X3 + 0.16X4 + 0.02Z + 12

X2 = 0.11X1 + 0.30X2 + 0.17X3 + 0.18X4 + 0.04Z + 15

X3 = 0.20X1 + 0.25X2 + 0.13X3 + 0.14X4 + 0.20Z + 150

X4 = 0.40X1 + 0.21X2 + 0.40X3 + 0.22X4 + 0.01Z +10

Z = 0.9*0.03X1

The solution is:

X1=198.446

X2=129.175

X3=324.007

X4=278.754

Z=5.358