a business needs to hire a social media consultant, and there are three from which to choose. the first…

a business needs to hire a social media consultant, and there are three from which to choose. the first consultant charges $50 per hour worked. the second consultant charges $20 per hour worked, plus a flat fee of $300. the third consultant charges only a flat fee of $650. for which number of hours worked would the second consultant be the least expensive? select all that apply. a. 5 b. 8 c. 11 d. 14 e. 17 f. 20

a business needs to hire a social media consultant, and there are three from which to choose. the first consultant charges $50 per hour worked. the second consultant charges $20 per hour worked, plus a flat fee of $300. the third consultant charges only a flat fee of $650. for which number of hours worked would the second consultant be the least expensive? select all that apply. a. 5 b. 8 c. 11 d. 14 e. 17 f. 20

Answer

Answer:

A. 5, B. 8

Explanation:

Step1: Define cost - functions

Let $x$ be the number of hours worked. The cost of the first consultant $C_1 = 50x$. The cost of the second consultant $C_2=20x + 300$. The cost of the third consultant $C_3 = 650$.

Step2: Compare $C_2$ and $C_1$

We want $C_2<C_1$, so $20x + 300<50x$. Subtract $20x$ from both sides: $300 < 30x$. Divide both sides by 30: $x>10$.

Step3: Compare $C_2$ and $C_3$

We want $C_2<C_3$, so $20x+300 < 650$. Subtract 300 from both sides: $20x<350$. Divide both sides by 20: $x < 17.5$.

Step4: Find valid values of $x$

Combining the two inequalities $10 < x<17.5$, for the given options, when $x = 11,14,17$ the second - consultant is not the least expensive. When $x = 5$ and $x = 8$, the second consultant is the least expensive.