ou were named District Manager of the Month at BeBop Records due to a hiring study you conducted. Your study showed that each of 30 salespersons that you supervise average $50,000 in sales each month. Your study also showed that for each new salesperson hired, the average monthly sales would decrease $1,000.
You presented this study to the company's CEO. What is the maximum average sales the company can expect with all it's salespersons?
This problem is poorly worded. The total sales if x new people are hired is
(50000-1000x)(30+x)
Find the vertex of that parabola to determine how many new people should be hired, to produce maximum total sales.
But clearly, the average sales do nothing but decrease, since each new hire lowers the average.
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To determine the maximum average sales the company can expect with all its salespersons, you'll need to consider the impact that hiring new salespersons has on the average monthly sales. Based on the information given in the question, we know that each of the 30 salespersons you supervise currently average $50,000 in sales each month, and that for each new salesperson hired, the average monthly sales would decrease by $1,000.
To calculate the maximum average sales, we need to account for the decrease in sales for each new salesperson hired. Since hiring additional salespersons decreases the average sales by $1,000, we can calculate the maximum average sales by subtracting $1,000 for each new salesperson from the current average sales of $50,000.
Since there are 30 salespersons currently, if we were to hire "x" number of new salespersons, the total number of salespersons would be 30 + x. We can then subtract the decrease in average sales for each new salesperson from the current average sales to find the maximum average sales:
Max Average Sales = Current Average Sales - (Decrease in Sales per New Salesperson * Number of New Salespersons)
Max Average Sales = $50,000 - ($1,000 * x)
So, the formula to calculate the maximum average sales based on the number of new salespersons hired would be Max Average Sales = $50,000 - ($1,000 * x), where "x" represents the number of new salespersons hired.
Unfortunately, the question does not provide information on the number of new salespersons being hired, so it is not possible to calculate the exact maximum average sales without that information.