SOLUTION: Stan can be paid in one of two ways Plan A - $900 per month plus a 10% commission on all sales or Plan B - $1200 per month plus a 15% commission on all sales over $8000 If w

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Question 323550: Stan can be paid in one of two ways
Plan A - $900 per month plus a 10% commission on all sales
or
Plan B - $1200 per month plus a 15% commission on all sales over $8000
If we assume that Stan always sells more than $8000, when is plan B better?
The book says for values > $18,000.....but I don't get it....

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is a linear relation in both plans between
Earnings/month = (flat wages)/month + (commission earned/month)
given:
plan A:
E+=+900+%2B+.1s
plan B:
E+=+1200+%2B+.15%2A%28s+-+8000%29
The 2nd term doesn't come into play until s+%3E+8000, otherwise
Stan would be penalized if sales were less than $8000
The question is: when is E the same under both plans?
900+%2B+.1s+=+1200+%2B+.15%2A%28s+-+8000%29
900+%2B+.1s+=+1200+%2B+.15s+-+1200
.05s+=+900
s+=+18000
When sales are over $1800, plan B is better
I can plot these plans with E = vertical axis in thousands of dollars
and s = horizontal in thousands of dollars
+graph%28+500%2C+500%2C+-1%2C+25%2C+-1%2C+4%2C+.9+%2B+.1x%2C++.15x++%29+