Alexis runs a small business and creates recordings of her friend’s skateboard stunts. she puts the recordings onto blu-ray and sells them online. she realized that the average cost of each blu-ray depends on the number of blu-rays she creates, because of the fixed cost. the cost of producing x blu-rays is given by b(x) = 1250 +1.75x
1) alexis wants to figure out the price to charge friends for the blu-rays. she doesn’t want to make money at this point since it is a brand new business, but does want to cover her costs. suppose alexis created 50 blu-rays. what is the cost of producing those 50 blu-rays? how much is it for each blu-ray?
2) what is the total cost and cost per blu-ray for 100, 1000, and 10,000?

Question 1)

a) What is the cost of producing those 50 blu-rays?

b) How much is it for each blu-ray:

Question 2) What is the total cost and cost per blu-ray for 100, 1000, and 10,000?

Number of blu-rays     Total cost        Cost per blu-ray

a) 100                               1,425                  14.25

b) 1000                             3,000                3.00

c) 10,000                          12,500               1.88

Explanation:

Question 1) What is the cost of producing those 50 blu-rays? How much is it for each blu-ray?

The cost of producing the blu-rays is modeled by the function

Thus, to calculate the cost of producing 50 blu-rays you just substitute 50 for x in the function and compute:

To calculate the cost of each of the 50 blu-rays, you divide the total cost (1,337.50) by the number of blu-rays (50).

Question 2) What is the total cost and cost per blu-ray for 100, 1000, and 10,000?

The general expresssion to calculate the total cost per blu-ray unit is found by dividing the total cost, B(x) = 1250 + 1.75x, by the number of blu-rays, x:

To calcualte the total cost and cost per blu-ray, substitute 100, 1000, and 10,000 in the expressions:

# of blu-rays     Total cost                                    Cost per blu-ray

100                    1250 + 1.75 (100) = 1,425             1,425/100 = 14.25

1000                  1250 + 1.75 (1000) = 3,000          3000/1000 = 3.00

10,000               1250 + 1.75(10,000) = 12,500      18,750/10,000 = 1.875

As you see, the cost per blu-ray decreases as the number of blu-rays increases, and at the limit (for a huge amount of blu-rays) the cost of blu-rays goes closer to 1.75, which is the unit rate of change of the function (the slope of the graph).

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step-by-step explanation:

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