Question 645252
Been out of school for a long time.  Need detailed, step-by-step assistance in solving the following problem:

Base salary = $2000 per month
Commission paid at 8% on all sales over $7000 during the month

Based on the above info, answer question: How much must the salesperson sell in one month to earn a total of $4000 for the month?


Is this break-even analysis?


Let the amount of sales he needs to have, in order to earn $4,000 for the month, be s

Then:

{{{E(s) = 2000 + .08s}}}, if s > $7,000
{{{E(s) = 2000}}}, if {{{s<=7000}}}


In order to make $4,000 then $2,000 will be base and the other $2,000 will be from commissions. This means we use the 1st equation, since he definitely will have to have a sales amount that exceeds $7,000: 


E(s) = 2,000 + .08s, with E(s) = 4,000


We then have: 

4,000 = 2,000 + .08s


4,000 - 2,000 = .08s ------ Solving for s, or sales amount


2,000 = .08s


s, or amount of sales = {{{2000/.08}}}, or ${{{highlight_green(25000)}}}


No, break-even analysis is the point at which revenues equal expenses.


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