Final answer:
The increase in the objective function coefficient in an optimization problem causes the optimal solution to change. It affects the contribution of a variable to the total cost or profit, reflecting the variable's new importance in achieving the best outcome within the set parameters.
Step-by-step explanation:
When the objective function coefficient increases in an optimization problem such as a linear programming model, the optimal solution, which is the best outcome within the given set of parameters, tends to change. This coefficient represents the contribution of a variable to the overall value of the objective function, typically related to cost or profit. As a firm produces higher quantities of output, costs increase due to higher quantities of inputs required which means more dollars to spend, suggestive of the cost behavior in a production setting.
Similarly, considering variable costs and their relation to production, as production commences, total and variable costs rise. This rise aligns with the concept of diminishing marginal productivity. For example, adding more workers may initially increase output significantly, but beyond a certain point, each additional worker contributes less to output than the previous one, leading to a reduction in efficiency and an increase in variable costs. If the objective function coefficient for one of the variables increases, it means that the contribution of that variable to cost or profit has increased; hence, in the context of a linear programming model, the decision variable linked to it would be adjusted to reflect the new cost/profit structure in search for a new optimal solution.