Karen can be paid in one of two ways for selling insurance policies:
Plan A:A salary of $750 per month, plus a commission of 10% of sales.
Plan B:A salary of $1000 per month, plus a commission of 8% of sales in excess of $2000.
For what amount of monthly sales is plan A better than plan B if we can assume that sales are always more than $2000?
Plan A: Salary $750 + .10 of sales
Plan B: Salary $1,000 + .08 of sales > $2,000
x = dollar amt of sales
750 + .10x > 1000 + .08(x - 2000)
750 + .10x > 1000 + .08x - 160
750 + .10x > 840 + .08x
0.02x > 90
x > 4500
Plan A better when sales > $4500
That was a huge help. Thank you!!!
You're welcome :)
Well, well, well! Karen has some interesting payment options, huh?
Let's crunch the numbers and figure out when Plan A becomes the superior choice over Plan B. We need to find the threshold where the salary + commission in Plan A is greater than the salary + commission in Plan B.
For Plan A, the monthly salary is $750, and the commission is 10% of sales.
For Plan B, the monthly salary is $1000, and the commission is 8% of sales in excess of $2000.
So, we can set up an equation where the earnings from Plan A are equal to the earnings from Plan B:
750 + 0.10s = 1000 + 0.08(s - 2000)
Here, "s" represents the monthly sales.
Let's simplify this equation:
750 + 0.10s = 1000 + 0.08s - 160
Now, let's combine like terms:
0.10s - 0.08s = 1000 - 750 + 160
0.02s = 410
To solve for "s", let's divide both sides by 0.02:
s = 410 / 0.02
s = 20500
So, if Karen's monthly sales exceed $20,500, then Plan A would be the better option for her. Otherwise, Plan B would be the way to go!
Hope that helps, and may Karen's sales be sky-high!
To determine for what amount of monthly sales Plan A is better than Plan B, we need to find the point at which the earnings under Plan A exceed the earnings under Plan B.
In Plan A, Karen's total monthly earnings are the sum of her salary ($750) and her commission (10% of sales).
In Plan B, Karen's total monthly earnings are the sum of her salary ($1000) and her commission (8% of sales in excess of $2000).
Let's express these two plans mathematically:
Plan A earnings (E_A) = $750 + 0.1s
Plan B earnings (E_B) = $1000 + 0.08(s - $2000)
where "s" represents the monthly sales.
Now, we need to find the point at which E_A is greater than E_B:
E_A > E_B
$750 + 0.1s > $1000 + 0.08(s - $2000)
$750 + 0.1s > $1000 + 0.08s - $160
$750 - $1000 + $160 > 0.08s - 0.1s
-$90 > -0.02s
90 < 0.02s
90/0.02 < s
4500 < s
So, Plan A is better than Plan B for monthly sales that are greater than $4500.