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?

Explanation:

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.

1) the stages a new product goes through from beginning to end, i.e., the stages that a product passes through from introduction through growth, maturity, and decline. 2) the time from initial research and development to the time at which sales and support of the product to customers are withdrawn. 3) the period of time during which a product can be produced and marketed profitably.

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