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A novel method for obtaining infrared intensities of vibration-rotation transitions in diatomic molecules will be presented. The method involves extracting a maximum amount of information about the dipole-moment function from available electric-resonance studies of the vibrational dependence of the molecular dipole moment. By a straightforward application of linear programming, this information which may be supplemented by available ab initio calculations of the dipole moment function, is used to obtain error limits to the necessary transition matrix elements. Numerical results will be presented in the case of the lithium hydrides. We obtain the absolute and relative intensities of the P and R branches to within 10%.