2. Earth Care, Inc. sells product relying on personal contact salespeople (advis

Question

2. Earth Care, Inc. sells product relying on personal contact salespeople (advisors). They have tracked sales by territory with a territory defined as a geographic area containing approximately 200,000 people. It shows the following: Sales pe advisor Sales-of 125 125 125 125 124 122 116 1000 1240 1470 1690 18 2050 217 The equation for the curve that best fits the data is y--2.7089x3 +161.4x-93.78 with an Ra0,9991 14 102 94 Each advisor gets a basic annual salary of $70,000 and a commission of 10% on sales. Earth Care makes 20% gross profit on sales after commissions. Their decision variable is the number of advisors to assign to each 200,000 person sales territory. They can assign 5, 10, or 20 advisors to each territory. Which assignment maximizes revenue to the representative? Which assignment maximizes gross profit for the firm?

Explanation / Answer

It can be clearly seen from the data that when the number of advisors are less the sales per advisor is 125. Sales per advisor is 125 till there are 8 advisors and as it reaches 10 advisors then the sales per advisor drops to 124. Similarly there is consistent drop in the number of sales if the number of advisors keep on increasing further.

And so to maximize the revenue to the representative 5 advisors out of the given choice of 5, 10 and 20 is best with 125 sales per advisor and so the profit.

To maximize the gross profit to the firm it requires maximum sale and number of advisors as they have to be paid their fixed salary.

From above table it is clear that when number of advisors increases from 5 to10 the salary doubles and the profit of the firm nearly doubles from 125 to 248. But with further increase from 10 to 20 advisors, the salary doubles means expenses are increased but the profit of the firm not actually doubles it only increases from 248 to 410.

So in order to maximize the profit the firm should go for 10 advisors.

Sales No of advisors Salary 70000 per advisor Profit of firm in number of sales 625 5 350000 125 1240 10 700000 248 2050 20 1400000 410

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