Question

You are selling a product in an area where 30 % of the people live in the city and the rest live in the suburbs. Currently 20 % of the city dwellers user your product and 10 % of the suburbanites use your product. You are presented with two new sales strategies the first will increase your market share in the suburbs to 15 %. The second will increase your market share in the city to 25 %. Which strategy should you adopt? What percentage of the people who own your product are city dwellers before your new sales drive?

Answer 1

Answer:

a). I would adopt the increase in market share in the suburbs by 15 % since the number of final suburbs dwellers who will use my product is (0.0805 x) which is  greater than final city dwellers' (0.075 x)

b). The total percentage of people who are city dwellers who own your product before the new sales drive=46.15%

Explanation:

a). We can make the following expressions;

Total number of both city dwellers and suburb dwellers=x

City dwellers=30% of x=(30/100)×x=0.3 x

Suburb dweller=70% of x=(70/100)×x=0.7 x

Total number of city dwellers who use your product initially=(20/100)×0.3 x=0.06 x

Total number of suburb dwellers who use your product initially=(10/100)×0.7 x=0.07 x

If we increase the market share in the suburbs by 15%

Number of suburb dwellers=0.07 x+(15/100)×0.07 x

Number of suburb dwellers=(0.07 x+0.0105 x)=0.0805 x

If we increase market share in the city by 25%

Number of city dwellers=0.06 x+(25/100)×0.06 x

Number of city dwellers=(0.06 x+0.015 x)=0.075 x

I would adopt the increase in market share in the suburbs by 15 % since the number of final suburbs dwellers who will use my product is (0.0805 x) which is  greater than final city dwellers' (0.075 x)

b). Percentage of city dwellers that own your product

Percentage=(Initial number of city dwellers/Total number of people)×100

Percentage=0.06 x/(0.06 x+0.07 x)=(0.06 x/0.13 x)×100=46.15%

The total percentage of people who are city dwellers who own your product before the new sales drive=46.15%