Question 1036352: Curt can be paid in one of two ways for the furniture he sells. Plan A: Salary of $800 per month, plus a commission of 10% of sales. Plan B: Salary of $900 per month, plus a commission of 15% of sales in excess of $6000. For what amount of monthly sales is plan B better than plan A, assuming Curt's sales are always more than $6000?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the monthly sales figure.
plan A revenue is equal to 800 + .10 * x
plan B revenue is equal to 900 + .15 * x - .15 * 6000 = 900 + .15 * x - 900 = .15 * x, because the 900 monthly salary is erased by him losing 15% commission on the first 6000 of sales.
you get:
plan A pays 800 + .10 * x
plan B pays .15 * x.
if plan B revenue is greater than plan A revenue, your equation becomes:
.15 * x > 800 + .10 * x
subtract .10 * x from both sides of this equation to get .05 * x > 800
divide both sides of this equation by .05 to get x > 800 / .05 = 16,000.
plan B revenue sill be better when his sales are greater than 16,000 per month.
to check if this is true, calculate revenue in both plans for sale = 11,000 per month, 16,000 per month, and 21,000 per month.
any amount below 16,000 or above 16,000 will do.
i just picked 11,000 and 16,000 at random.
no special reason.
when sales are 11,000 per month, ...
plan A pays 800 + .10 * 11,000 = 800 + 1100 = 1900.
plan B pays 900 + .15 * 5,000 = 900 + 750 = 1650.
plan A pays better.
when sales are 16,000 per month, ...
plan A pays 800 + .10 * 16,000 = 800 + 1600 = 2400.
plan B pays 900 + .15 * 10,000 = 900 + 1500 = 2400.
plan A and plan B pay the same.
when sales are 21,000 per month, ...
plan A pays 800 + .10 * 21,000 = 800 + 2100 = 2900.
plan B pays 900 + .15 * 15,000 = 900 + 2400 = 3150.
plan B pays better.
the breakeven point is when sales are 16,000 per month.
plan A pays better when sales are less than 16,000 per month.
plan B pays better when sales are greater than 16,000 per month.
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