Question

a 2. Singh makes a base salary of S2400 per month. Once he reaches S50000 in total sales, he carns an additional 5% commission (salary) on the amount by which his sales exceed $50000. Lets be the amount of his total sales for the month and G(s) be the amount of his salary for the month. Answer either Part (a) OR Part (b) below. a. 4 points. Graph G(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) cach axis represents. OR b. 4 points. Write a piecewise-defined function to model the Singh's total monthly salary G(s) (in dollars) as a function of the amount of sales

Answer 1

Function and Their Graph: Given, Base Salary = $2400 per month Commission=5% on amount exceeds $50,000 (a) We have to graph the function G(s) of his monthly salary. Since the base salary is 2400 so graph is constant up to the sales of $50,000. So it is a straight line y = 2400. Lets be the total sales then the amount exceeding $50,000 is s-50000. So the commission amount is given as follows: Commission = (s – 50000)x= 5 = 0.05( s-50000) 100

Therefore, the salary after sales exceeds $50,000 is given as follows: G(S) = 2400+ 0.05( s-50000) = 0.05+4900 Therefore, the graph is given as follows: 6000+ Salary(in dollars) 5000+ 4000+ 3000+ 2000+ 1000+ 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Sales(in dollars)

(b) Piecewise Defined Function is given as follows: G(S) = 2400, 0.05s-100 0<3 < 50000 S> 50000