Curt can be paid in one of two ways for the sales he generates:
Plan A: 900$ per month plus 10% sales commission.
Plan B: $1200 per month plus 15% commission on sales above $8,000.
Assuming he always exceeds $8,000 in sales, for what amount interval of $ sales is Plan B better?
900 + .1 x = 1200 + .15(x - 8,000)
is breakeven point. Above that take the 15%
So I distribute the .15 and then solve for x?
yes
why did you put .1% instead of .10%?
They are both the same.
10% = 10/100 = .10 = .1
To determine the amount interval of sales where Plan B is better, we need to compare the earnings under both plans.
Let's first calculate Curt's earnings under Plan A:
Earnings from the monthly salary: $900
Earnings from the sales commission: 10% of sales
Now let's calculate Curt's earnings under Plan B:
Earnings from the monthly salary: $1200
Earnings from the sales commission: 15% of the sales above $8,000
Now, we can set up an equation to find the amount interval where Plan B is better:
Earnings under Plan B > Earnings under Plan A
Let's denote the sales as 'x' in the equation:
$1200 + (15% * (x - $8,000)) > $900 + 10% * x
Simplifying the equation:
$1,200 + 0.15(x - $8,000) > $900 + 0.1x
$1,200 + 0.15x - $1,200 > $900 + 0.1x
0.15x - $0.15($8,000) > $900 + 0.1x
0.15x - $1,200 > $900 + 0.1x
0.15x - 0.1x > $900 + $1,200
0.05x > $2,100
Divide both sides of the inequality by 0.05:
x > $42,000
Therefore, for sales above $42,000, Plan B is better.
In conclusion, Plan B is better for sales above $42,000.