SOLUTION: The total cost,C,(in thousands of dollars) to make reading glasses is a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11

Question 1200730: The total cost,C,(in thousands of dollars) to make reading glasses is
a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11.61
a)Find the marginal cost at the production level of 21 thousand and choose the correct units
b)What is the average cost at the same production level?

Answer by GingerAle(43) (Show Source): You can put this solution on YOUR website!
**a) Find the Marginal Cost**
1. **Find the derivative of the cost function:**
* C'(u) = d/du (-0.02u² + 2.33u + 11.61)
* C'(u) = -0.04u + 2.33
2. **Evaluate the derivative at u = 21 (production level of 21 thousand pairs):**
* C'(21) = -0.04 * 21 + 2.33
* C'(21) = 1.49
**Therefore, the marginal cost at a production level of 21 thousand pairs of glasses is $1.49 thousand per thousand pairs (or $1490 per thousand pairs).**
**b) Find the Average Cost**
1. **Calculate the total cost at u = 21:**
* C(21) = -0.02 * (21)² + 2.33 * 21 + 11.61
* C(21) = -8.82 + 48.93 + 11.61
* C(21) = 51.72 thousand dollars
2. **Calculate the average cost:**
* Average Cost = Total Cost / Number of Units
* Average Cost = 51.72 thousand dollars / 21 thousand pairs
* Average Cost = 2.46 dollars per pair
**Therefore, the average cost at a production level of 21 thousand pairs of glasses is $2.46 per pair.**

RELATED QUESTIONS
A restaurant manager wants to order more glasses. The ratio of the number of water... (answered by TimothyLamb)

A juice seller sells juice in small, medium and large glasses. The cost of a small... (answered by Theo)

A juice seller sells juice in small, medium and large glasses. The cost of a small... (answered by stanbon)

The science teacher ordered 7 magnifying glasses that cost $1.25 each and 7 pairs of... (answered by ewatrrr)

In a class, 2/5 of the boys wear glasses and 1/3 of the girls wear glasses. If the ratio... (answered by stanbon)

a shop owner orders a number of drinking glasses which she pays R300, while unpacking... (answered by ikleyn)

the ratio of the number of pupils who wear glasses to the total number of pupils in the... (answered by greenestamps,math_tutor2020,ikleyn,josgarithmetic)

Out of a total of 400 students in a school, 245 of them wear glasses. What percent of the (answered by ikleyn,Edwin McCravy,MathTherapy)

in a class 2\5's of the students wear glasses. if ten students wear glasses,how many... (answered by rfer)