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

To calculate Scarlett's profit for selling ponchos, subtract her total expenses from her total revenue using the functions provided. For a specific number of ponchos, plug that number into both the revenue and expense functions and subtract the results.

Step-by-step explanation:

The student's question deals with the calculation of profit for a business venture, specifically for selling batches of designer ponchos. Given the revenue function R(n) = 20n and the expense function E(n) = 10 √{n}, the profit that Scarlett makes from producing and selling a batch of n ponchos can be calculated by subtracting the total expenses from the total revenue, which is P(n) = R(n) - E(n). To find Scarlett's profit for a specific number of ponchos, simply plug the value of n into both functions and perform the subtraction.

For example, if Scarlett wants to calculate the profit for selling 5 ponchos, the revenue would be R(5) = 20(5) = $100, and the expenses would be E(5) = 10√5. Scarlett's total profit for 5 ponchos would then be P(5) = $100 - 10√5.

Answer 2

Write a formula for P(n) in terms of R(n).

R(n) - E(n)

Write a formula for P(n) in terms of n.

20n -
`10√(n)`

Step-by-step explanation:

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