The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as:

additivity assumption

Explanation:

In order to find out an optimum solution, the Linear Programming problem is constructed by selecting the best option from the set of possible options available to the decision maker. Assumption means to simplify a condition that is considered to be true in the system being examined, to make the model computationally efficient and mathematically solvable

The basic assumptions of linear programming are Proportionality, Additivity, Divisibility, Certainty.

Additivity Assumption:

Additivity Assumption means that the total value of the objective function and each constraint function is determined by the sum of the individual contributions from each variable. This means that additivity assumption states that the total profit or cost of the objective function equals the sum of the individual variable (product) profits. Likewise, the overall amount of resources used equals the resources used individually by each variable (product). In other terms, it implies that the variable is independent of other decision variables i. e. there is no interaction between the decision variables.