The Wentworth Company Manufactures Modular Furniture for the Home, and Uses

The Wentworth Company manufactures modular furniture for the home, and uses a monthly variance-reporting system to control costs of the manufacturing departments. Edward Collins is the supervisor of the Assembly Department and is reviewing the monthly variance analysis for November, which shows a significant cost overrun (i.e., unfavorable cost variance). Collins has gathered the following information to assist him in deciding whether or not to investigate the unfavorable cost variance for the Assembly Department:
Estimated cost (I) to investigate the variance $4,000
Estimated probability that the Assembly Department is operating properly, that is,
the probability that the observed variance is a random event = (1 − p) = 90%
If the Assembly Department is operating out of control (i.e., improperly):
Estimated cost (C) to correct the process = $8,000
Estimated loss (L) if the observed variance is the result of a nonrandom cause
but the company fails to investigate = $40,000
Required:
Recommend whether Wentworth Company should investigate the observed unfavorable cost variance. Support your answer by:
1. Preparing a 2 × 2 payoff table for use in making the decision. Let the rows in your table represent possible managerial actions (Investigate vs. Don't Investigate) and the columns of your table represent possible states of nature (Random vs. Nonrandom).
2. Computing the expected value (to the nearest whole dollar) of the cost of each of the two actions that management can take: investigate the variance, or do not investigate the variance. (Let p = the probability that the process is out of control, that is, the probability of a nonrandom variance, and (1 − p) = the probability that the process is in control, that is, the probability that the observed variance is due to random causes.)