The agent gets 35 of the first 5000000 The agent gets7 of th

The agent gets 3.5% of the first $5,000,000 The agent gets7% of the next $5,000,000 The agent gets 10.5% of the remaining value Write a piecewise-defined function C that specifies the agents cut of a contract worth x dollars.

Solution

agent gets 3.5% of the first $5,000,000

Agents cut

f(x) = 0.035*x for x<=5000000 (1)

agent gets7% of the next $5,000,000

Out of this upto $5,000,000 part 1 is applicable + for 5000000<x<=10000000 7% is applicable

= 0.03*5000,000 +0.07(x -5000,000) for 5000000<x<=10000000

= 0.07x -2000,000   for 5000000<x<=10000000

The agent gets 10.5% of the remaining value

for x<= 5000000 3.5% is applicable +x> 10000,000 upto $10,000,000 7% is applicable +remaining at 10.5% is applicable

f(x) = 0.035(5000000) +0.07(10000000 -5000000) +0.05(x- 10000000)

= 175000 + 350000 + 0.05x -500000

=0.05x + 25000 for x> 10000,000