Final answer:
Not every change in an objective function coefficient leads to a new optimal solution, as it depends on the model's specifics and whether the change affects the constraint boundaries. However, significant changes can cause a shift in the optimal solution. The budget constraint framework emphasizes the comprehensive effects of changes in income and price on consumption, including both income and substitution effects.
Step-by-step explanation:
Not every change in the value of an objective function coefficient will lead to a changed optimal solution in a linear programming problem. The impact depends on the specific characteristics of the model, including the constraints and the current solution. A small change might occur within the bounds of the existing optimal vertex (corner point), especially if it does not cause the current solution to cross a constraint boundary. However, if the change is significant enough to alter the position of the optimal vertex on the feasible region, the optimal solution will indeed change.
The budget constraint framework underscores the importance of considering the full spectrum of economic behavior changes in response to variations in income or price. Changes in price can result in both a substitution effect, where consumers might substitute a good for another due to a relative change in price, and an income effect, where the real income of consumers changes, influencing their purchasing power. Similarly, a change in income can lead to an alteration in consumption patterns due to an income effect but is not associated with a substitution effect.
For example, efficiency is always less than 1, whereas coefficients of performance are greater than 1, which suggests that checking reasonableness is an essential part of the problem-solving process.