Question

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

Answer 1

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

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 >
`(1)/(4)`