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Programming Models for use of the Lofgreen-Garrett Net Energy System in Formulating Rations for Beef Cattle

Economic Research Service, U.S. Department of Agriculture 20250

Abstract

LOFGREEN and Garrett have proposed a net energy system for beef cattle in which the net energy requirements and feed values are separated into two components: net energy for maintenance (NE_m) and net energy for production of gain in body weight (NEg). (Lofgreen and Garrett, 1968a, b).

Their system presents some difficulties in linear programming because each of the two energy equations involved applies only over a certain portion of total feed intake.

The purpose of this paper is to present models for dealing with the interdependent nature of the two energy equations of the Lofgreen-Garrett net energy system in ration programming.

For the purpose of this paper the Lofgreen-Garrett system is stated in the form shown inequations (1) and (2).

(1) a a_1jX_j= W^0.75

(2) (1—a a_2jX_j)=(bg+cg²) W^0.75

Where a is the proportion of daily feed intake used for maintenance, (1—a) is the proportion of daily feed intake available for production; a_1j, a_2j are, respectively, the NE_m and NE_g values of the jth feed ingredient; X_j is the quantity of the jth ingredient consumed per day; W and g are body weight and gain per day, respectively.

¹ The author is grateful to Richard E. Vaile, Gene Nelson, Dale R. Waldo and D. C. Church for helpful comments on earlier drafts of this article.