Q.In a LPP, the objective function is always _________.

In a Linear Programming Problem the objective function $Z = c_1 x_1 + c_2 x_2 + \dots + c_n x_n$ must be linear — every variable to the first power only (degree $1$), with no squares, products or other nonlinear terms. This linearity is what makes it linear programming, and what let …

The name Linear Programming itself fixes the answer: the objective must be linear. A linear objective changes at a constant rate as you move in any fixed direction, and it is exactly this property that makes the graphical corner-point method work.

1. The ingredients of an LPP. Decision variables, a linear objective function to maximise or minimise, and linear constraints. If the objective (or a constraint) is not linear, it is not an LPP.

2. What "linear" means for the objective. A linear function of the variables has the form

where each $c_i$ is a constant and every variable appears only to the first power — no $x_i^2$, no $x_i x_j$, no $\sin x_i$, no $1/x_i$. Its degree is $1$. …

Method: Deciding what kind of function the objective must be

For a "the objective function is always ___" style blank, reason from the name of the subject and the property that makes its solution method work.

The reasoning pattern

Step 1: Read the name.

It is linear programming, so both the objective and the constraints must be linear.

Step 2: State what "linear" means precisely.

A linear (degree-one) objective has the form

each term a constant times a variable to the first power only -- no $x^2$, no $x_i x_j$, no $\sin x$, no $\sqrt{x}$. …