When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $17,000 a year, with a commission of 12% of your sales

Option B: Base salary of $20,000 a year, with a commission of 5% of your sales

How much jewelry would you need to sell for option A to produce a larger income?

Question

Business

Sullivan Nunez

5 July, 08:10

When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $17,000 a year, with a commission of 12% of your sales

Option B: Base salary of $20,000 a year, with a commission of 5% of your sales

How much jewelry would you need to sell for option A to produce a larger income?

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Answers (1)

Know the Answer?

Melanie May · Answer 1

To find the amount of sales for option A to produce a larger income, first find a model for both options.

Firstly, Let A (s) be the salary in dollars produced per year from option A.

Since the salary increases by 12 cents for each additional dollar in sales, A (s) is a linear function with a rate of change, or slope, of. 12

The initial value is the base salary per year or $17000

There the linear model is A (s) = 0.12s + $17000 ... (1).

Secondly, Let B (s) be the salary in dollars produced per year from option B by selling

Since the salary increases by 5 cents for each additional dollar in sales, B (s) is a linear function with rate of change, or slope, of. 05.

The initial value is the base salary per year or $20000.0. The linear model is B (s) = 0.05s + $20,000 ... (2)

To find the sales needed so that the salary from option A is greater than option B, find the set of s-values that make the output values from equation (1) greater than the output values from equation (2).

A (s) = 0.12s + $17000 > B (s) = 0.05s + $20,000

0.12s + $17000 >0.05s + $20,000

0.12s - 0.05s > $20,000-$17000

0.07s >$3000.00

Therefore s > $42,857.14

Therefore, more than $42,857.14 would need to be sold for option A to produce a larger income than option B.