Question

2. Piecewise functions. Terry earns a base salary of $2100 per month. Once he reaches $40000 in total sales, he earns an additional 5% commission (salary) on the amount of sales over $40000. Lets be the amount of his total sales for the month and M(s) be the amount of his salary for the month. (For instance, if he had sales of $42000 for the month, he would earn a salary of $2100 and 5% of $2000, since $42000 is $2000 more than $40000.) a. [5 pts) Graph M(s) for s values between $0 and $100000 in sales. Indicate your scale on both the horizontal and vertical axes, and be sure to label what quantities (salary or sales) each axis represents. b. (2 pt) If Terry had $78000 in sales, how much was his salary for that month? c. [2 pts) If Terry's total salary for a month was $3900, how much were his total sales for that month? d. (2 pts] Compute M(25000) and interpret what this means in the context of the problem in terms of the monthly salary and the sales).

Answer 1

a.) the function can be written as:

M(s) = 2100 , when 0<=s<=40000

= 2100 + 0.05(s-40000) , when s>40000

graph of M(s) is:

80000 60000 -40000 20000 (0, 2100) (400000 2100) -20000 0 20000 40000 60000 80000 100000 120000 1400

scale: X-axis (sales) = 1 unit= $20000 sales

Y-axis (salary) = 1 unit= $20000 salary.

b.) when Terry had $78000, his sales above $40000, so M(s) according to above equation is:

M(78000) = 2100+ 0.05(78000-4000) = $4000

c.) given M(s)= $3900, s=?

M(s) = 2100 + 0.05(s- 40000)

=>3900 = 2100 + 0.05(s- 40000)

=> s- 40000= (3900-2100)/0.5

=> s= 3600+ 40000

=> s= $ 43600

d.) M(25000): (since 25000<40000)

M(78000) = 2100 = $2100

this means his sale in the month is $25000, and his salary in that month is $2100,