Q from 2009 CFAI mock exam. treasury future yield beta

Q from 2009 CFAI mock exam. The liability duration 6.83. The Asset Portfolio Duration 7.33, yield 5.21%. includes: US Treasuries $300 Millions, Duration 8.0, yield 4.52%, US corporate bonds $150 millions, Duration 6.0, yield 6.59%. Use US Treasury futures to hedge against interest rate risk. US Treasury futures duration 6.5, price $110,425, conversion factor for CTD bond 0.9177, yield beta 1.12. The number of future contracts needed to change the duration of portfolio is. (6.83-7.33)*450,000,000*.9177/(6.5*110,425)=-287.8 My question is why yield beta 1.12 is not used here. In notes, it says using Treasury future to hedge non Treasury bond is cross hedge, since two assets are not identical , basis is subject to change, their yield won’t move in tandem. The portfolio includes $150millions corporate bonds, the yield beta should be used. (6.83-7.33)*450,000,000*.9177*1.12/(6.5*110,425)