Piecerate systems are widely debated incentive payment plans

Piece-rate systems are widely debated incentive payment plans. In a recent study of loan officer effectiveness, the following piece-rate system was examined:

% of goal

reached

< 80

80

100

120

Incentive

n/a

$4,000 with an additional $125 added per percentage

point from 81–99%

$6,500 with an additional $125

added per percentage point

from 101–119%

$9,500 with an additional $125

added per percentage point

starting at 121%

If a loan officer makes 95% of his or her goal,

a. write the linear function that applies based on the incentive plan table.

b. In context, explain the y-intercept and slope.

Would you include an explanation with the answer so that I can use this to work through simular problems.

Solution

a) If the loan officer makes 95% of his goal

then incentive would be

in the range of above 80 and below 100.

Hence incentiveI = 4000+(x-80) 125

where x is the actual percentage of sales

i.e. Incentive = 4000+125x-10000

= 125x-6000

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Thus incentive = 125x-6000 is the linear function

y intercept =-6000 which implies if he does not make any sale his commission would be negative 6000.

Slope = increase for 1% sale = 125.