Question
A small business is considering hiring a new sales representative (sales rep) to market its product...
A small business is considering hiring a new sales representative (sales rep) to market its product in a nearby city. Two pay scales are under consideration.
Pay scale 1: Pay the sales rep a base yearly
salary of $14,400 plus a commission of 8% of total yearly
sales.
Pay scale 2: Pay the sales rep a base yearly
salary of $18,000 plus a commission of 5% of total yearly
sales.
(a) For each of the pay scales above, use a formula to express the
total yearly earnings for the sales rep as a function of total
yearly sales s. (Give percents in decimal form.)
| pay scale 1 |
T1(s) = |
| pay scale 2 |
T2(s) = |
(b) What amount of total yearly sales would result in the same
total yearly earnings for the sales rep no matter which of the two
pay scales is used?
$
(c) On the same screen, plot the graphs of the functions you made
in part (a). (Let T be total yearly earnings and
s the total yearly sales. Select the correct graph.)
(d) If you were a sales rep negotiating for the new position, under what conditions would you prefer pay scale 1?
when you expect total sales to exceed $27,692when you expect total sales to be below $27,692 when you expect total sales to exceed $120,000when you expect total sales to be below $120,000
Under what conditions would you prefer pay scale 2?
when you expect total sales to exceed $27,692when you expect total sales to be below $27,692 when you expect total sales to exceed $120,000when you expect total sales to be below $120,000
Homework Answers
Answer #1
A)
- Let s denote the total yearly sales and P1 = P1(s) denote the total yearly income under pay scale #1 and let P2 = P2(s) denote the total yearly income under pay scale 2.
So, P1(s) = 14,400+0.08s and P2(s) = 18,000+0.05s
B)as per the question , $120,000
- 14,400+0.08s = 18000+0.05s
- 0.08s-0.5s = 18000-14400
- 0.03s = 3600 = $120,000
C) We enter our formulas for P1 and P2 as Y1 and Y2 in the calculator. We set the horizontal range to be from 0 to 200,000 and let Zoomfit set the vertical range. The vertical range is from 10000 to 26000 and so we set the vertical scale as 1000. The two graphs are shown to the right. The line which is lower when s = 0 is P1(s). Picture is attached.
D) Prefer pay scale 1 when total sales are expected to exceed $120,000
- Prefer pay scale 2 when total sales are expected to be less than $120,000
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