Managerial Projections for Production and Marketing or The Case of the Suspicious Custome

B$.$R$.$ Harris arrived at work and found, as expected, the recommendations of H$.$E McRorie waiting on the desk. These recommendations would form the basis for a quarterly presentations regarding production levels for the next $3$ months. The projection would serve as a planning guide, ideally indicating appropriate levels for purchasing, inventory, and human resources in the immediate future. However, customers have a habit of not always behaving as expected, and so these forecasts were always difficult to prepare with considerable judgment $($guesswork$?)$ traditionally used in their preparation.

Harris and McRorie wanted to change this and create a more objective foundation for these necessary projections. McRorie had worked late analyzing the customer survey $($a new procedure they were experimenting with, based on responses of $30$ representative customers$)$ and had produced a draft report that read, in part:

We anticipate quarterly sales of $$1,478,598$ with projected sales by region given in the accompanying table. We recommend that production be increased from current levels of in anticipation of these increased sales...

Harris was uneasy. They were projecting a large increase from both the previous quarter $(32\mathrm{.}7\%)$ and from the same quarter last year $(44\mathrm{.}9\%).$ Historically, the firm has not been growing at near these rates in recent years. Along with that came a recommendation for increased production in order to be prepared for the increased sales. Why the hesitation? Because if these projections turned out to be wrong and sales did not increase, the firm would be left with expensive inventory $($produced at a higher cost than usual due to overtime, hiring of temporary help, and leasing of additional equipment$)$ with its usual carrying costs $($including the time value of money: the interest that could have been earned by wating to spend on the additional production$).$

Harris asked about this, and McRorie also seemed hesitant. Yet it seemed simple enough: Take the average anticipated spending by customers as reported in the survey and then multiple by the total number of customers in that region. What would be wrong with that? They decided to take a closer look at the data. Here is their spreadsheet, including background information $($the wholesale price the firm receives for each item and the number of active customers by region$)$ and the sampling results. Each of the $30$ selected customers reported the number of each item they plan to order during the coming quarter. The Value column indicates the cash to be received by the firm $($e$.$g$.,$ Customer $1$ plans to buy $3$ chairs at $$45$ and four bookshelves at $$65$ for a total value of $$395).$

Discussion questions:

$1)$ Would the average based procedure they are currently using ordinarily be a good method? Or is it fundamentally flawed.

$2)$ Take a close look at the data using summaries and graphs. What do you find? Revisit your answer to the first question.

$3)$ What would you recommend that Harris and McRorie do to prepare for their presentation this afternoon?