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Scarlett sells designer ponchos. The revenue, R, she makes from selling a batch of n ponchos is given by the function R(n)=20n, and the expenses, E, that she incurs from producing a batch of n ponchos is given by the function E(n)=10n√. Explain whether Scarlett earns a profit from producing and selling a batch of 9 ponchos.

A. Scarlett earns a profit because R(10)- E(10)=150
B. Scarlett earns a profit because R(10)/E(10)=6
C. Scarlett earns a profit because R(10)+E(10)=210
D. Scarlett does not earn a profit because E(10)-R(10)= -150

Respuesta :

Answer:

A. Scarlett earns a profit because R(10)- E(10)=150

Step-by-step explanation:

Revenue: R = 20n

Expenses: E = 10√n

Profit: P = R - E

            = 20n - 10√n

Profit is earned when Revenue > Expenses

20n > 10√n

÷10   ÷10      

2n >  √n

(2n)² >  (√n)²

4n² > n

4n² - n > 0

n(4n - 1)> 0

n > 0    and     4n - 1 > 0

                            n > [tex]\frac{1}{4}[/tex]

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