What is the objective function in the linear program with two decision variables X1 and X2?

• A. Max Z = X1 + X2
• B. Min Z = X1 + X2
• C. Max Z = 2X1 + 3X2
• D. Min Z = 2X1 + 3X2

Answer: (A)

A linear program optimizes a quantity called the objective, written as a linear combination of the decision variables. With two variables X1 and X2, the objective is typically Z = c1·X1 + c2·X2, and you choose whether to maximize or minimize Z.

The best choice here is the form that maximizes Z using both variables with simple unit coefficients: Max Z = X1 + X2. This fits the standard structure Z = c1·X1 + c2·X2 for a maximization problem, using both X1 and X2 with positive weights. The other options either switch to minimizing the objective or use different coefficients, which change the objective but aren’t the specified maximization form.