Question

The daily cost in dollars) to manufacture imitation oil paintings is given by the cost function C(x) = 0.2x2 - 5.5x + 300 where x is the number of oil paintings manufactured. What is the average cost when 60 paintings are manufactured?

A) $11.50 per painting
B) $5.29 per painting
C) $16.50 per painting
D) $18.50 per painting
E) $690.00 per painting

Answer 1

The average cost per painting when 60 paintings are manufactured is calculated using the cost function C(x) = 0.2x^2 - 5.5x + 300, resulting in an average cost of $11.50 per painting.

Step-by-step explanation:

To determine the average cost per painting when 60 paintings are manufactured, you would first use the given cost function C(x) = 0.2x2 - 5.5x + 300 and plug in the value of 60 for x. The cost function tells us the total cost for manufacturing x number of paintings. After calculating the total cost, we then divide this value by the number of paintings (60) to get the average cost per painting.

The calculation would be as follows:

1. Calculate the total cost for 60 paintings: C(60) = 0.2(60)2 - 5.5(60) + 300.
2. Simplify the equation: C(60) = 0.2(3600) - 5.5(60) + 300.
3. Further calculations lead to: C(60) = 720 - 330 + 300.
4. Which simplifies down to: C(60) = 690.
5. Finally, calculate the average cost by dividing the total cost by the number of paintings: 690 / 60.
6. The result is $11.50 per painting.

So the average cost when 60 paintings are manufactured is $11.50 per painting, which corresponds to option A).