The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high.
If she feels the chances of low, medium, and high demand are 50 percent, 20 percent, and 30 percent respectively, what are the expected annual profits for the number of beauticians she will decide to hire?
A) $54,000
B) $55,000
C) $70,000
D) $50,000
E) $154,000

Question

The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high.
If she feels the chances of low, medium, and high demand are 50 percent, 20 percent, and 30 percent respectively, what are the expected annual profits for the number of beauticians she will decide to hire? 
A) $54,000 
B) $55,000 
C) $70,000 
D) $50,000 
E) $154,000

Quizplus · Accepted Answer

Expected annual profits for each option are:

- One beautician: (0.5 x 25 + 0.2 x 45 + 0.3 x 60) x 1 = $38,500
- Two beauticians: (0.5 x 40 + 0.2 x 70 + 0.3 x 90) x 2 = $83,000
- Three beauticians: (0.5 x 50 + 0.2 x 80 + 0.3 x 100) x 3 = $151,500

Therefore, the best choice is to hire three beauticians for an expected annual profit of $151,500. However, since none of the answer choices match this result, the closest option is C, which is $70,000.

The New Owner of a Beauty Shop Is Trying to Decide