To determine if managers should be concerned about a $6000 production cost, we use the regression equation y = 1086.00 + 8.12x to estimate the volume that would result in this cost. We find that a production volume of approximately 605 units aligns with the cost of $6000. Costs exceeding this for the same volume would be cause for concern and warrant further investigation.
The student's question is about the application of regression analysis in accounting, particularly in estimating the cost associated with production volume.
Given the estimated regression equation y = 1086.00 + 8.12x, where y represents the total cost and x represents the production volume, the goal is to determine whether managers should be concerned if an accounting cost report shows an actual production cost of $6000 for the next month.
To assess this, we will use the regression equation to estimate what the total cost should be for the production volume that yields a $6000 cost.
Rearranging the equation to solve for x gives x = (y - 1086.00) / 8.12.
Substituting the given cost of $6000 into the equation, we calculate:
x = ($6000 - 1086.00) / 8.12
x ≈ 605.42 units
A production volume of approximately 605 units should result in a cost close to $6000, according to the regression equation.
If the cost report reflects this volume, the cost is in line with the expected cost based on the regression model.
However, if the production volume was significantly lower than 605 units, managers might need to investigate the reasons for the higher costs, considering factors such as economies of scale, diminishing marginal productivity, or other changes in production costs.