Question

Vasu's is a jewelry store specializing in handcrafted rings.

R(q)=−50q²+214q thousand dollars gives the monthly revenue that Vasu's brings in from selling q hundred rings, 0≤q≤2.5.
Use the marginal revenue to find the additional revenue from selling the 201st ring and finish the sentence of interpretation.
(Hint: Be careful with your units!)
The additional revenue from selling the 201st ring is __ dollars.

Answer 1

The additional revenue from selling the 201st ring at Vasu's jewelry store is $13,000. This is found by substituting q = 2.01 into the derivative of the revenue function R'(q) = -100q + 214.

Step-by-step explanation:

The given revenue function for Vasu's jewelry store is R(q) = -50q² + 214q thousand dollars, where q represents the number of hundred rings sold. To find the marginal revenue (MR), we need to take the derivative of the revenue function with respect to q.

The derivative of R(q) with respect to q is R'(q) = -100q + 214. To find the additional revenue from selling the 201st ring, we substitute q = 2.01 (since q is in hundreds of rings) into the marginal revenue function:

R'(2.01) = -100(2.01) + 214 = -201 + 214 = 13 thousand dollars.

Since the revenue is given in thousand dollars, the additional revenue from selling the 201st ring is 13 thousand dollars, or $13,000.

The interpretation is: The additional revenue from selling the 201st ring is $13,000.

Answer 2

The additional revenue from selling the 201st ring, calculated by finding the marginal revenue at q = 2.01 (for the 201st ring since q is in hundreds), is $13,000.

Step-by-step explanation:

To find the additional revenue from selling the 201st ring at Vasu's jewelry store, we need to calculate the marginal revenue (MR). The marginal revenue is the derivative of the total revenue function R(q) with respect to q.

The total revenue function is given by:

R(q) = -50q² + 214q thousand dollars.

First, let's find the derivative of R(q):

MR = dR/dq = -100q + 214.

Now, let's calculate the marginal revenue for the 201st ring. Remember that q is measured in hundreds of rings, so q = 2.01 for the 201st ring:

MR(2.01) = -100(2.01) + 214 = -201 + 214 = $13 thousand dollars.

Since the revenue is given in thousands of dollars, the additional revenue from selling the 201st ring is:

$13 thousand dollars = $13,000.

Therefore, the additional revenue from selling the 201st ring is $13,000 dollars.