Question

Scarlett sells designer ponchos. The revenue, RR, she makes from selling a batch of nn ponchos is given by the function R(n)=20nR(n)=20n, and the expenses, EE, that she incurs from producing a batch of nn ponchos is given by the function E(n)=10\cdot \sqrt{n}E(n)=10? n ? . Let PP be the total profit Scarlett makes from producing and selling a batch of nn ponchos

Answer 1

Answer: Scarlett must sell more than 1/4 of a batch in order to make a profit

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 > $\frac{1}{4}$