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. $54,000B. $55,000C. $70,000D. $80,000E. $135,000

NUMBER OF BEAUTICIANS            DEMAND  (thousands of dollars)

                                                        LOW        MEDIUM           HIGH

One                                                    50                75                100

Two                                                     0                100               100

Three                                               -100               70                300

Chance(probability) of occurrence = 50% low, 20% medium and 30% high

Expected Annual profit for 1 beautician = 0.5(50) + 0.2(75) + 0.3(100)

                                                                 = 25‬ + 15‬ + 30‬

                                                                 = 70 * 1000

                                                                = $70,000

Expected Annual profit for 2 beauticians = 0.5(0) + 0.2(100) + 0.3(100)

                                                                    = 0+ 20‬ + 30‬

                                                                    = 50 * 1000

                                                                    = $50,000

Expected Annual profit for 3 beauticians = 0.5(-100) + 0.2(70) + 0.3(300)

                                                                    = -50 + 14‬ + 90‬

                                                                    = 54 * 1000

                                                                    = $54,000

Therefore, the owner would go for 1 beautician, to maximize profit at all levels of demand because it has the highest expected annual profit at $70,000.

Step-by-step explanation:

Probability is expressed in decimal notation by multiplying by 100

i.e. 50% = 0.5

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step-by-step explanation: