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The RideEm Bicycles factory can produce 120 bicycles in a day at a total cost of $10,900. It can produce 140 bicycles in a day at a total cost of $11,400. What are the company's daily fixed costs (in dollars)

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Answer:

The company's daily fixed costs are $7900.

Explanation:

The normal cost function is linear and is the sum of the marginal cost and fixed cost:

Cost = marginal cost + fixed cost

Cost is normally a function of q (the number of units produced by a company) and its general equation (usually in slope-intercept form) is given by:

C(q) = mq + b, where

  • C is the cost per q units produced,
  • m is the marginal cost (change in cost per additional units made),
  • and b is the fixed cost (cost even when no units are made).

Finding the slope (m):

Since we're modeling cost as a function of quantity, we're starting with the points (120, 10900) and (140, 11400).

Now we can find the slope of the line that passes through these two points using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

  • m is the slope,
  • (x1, y1) is one point on the line,
  • and (x2, y2) is another point.

Now we can find the slope by substituting (120, 10900) for (x1, y1) and (140, 11400) for (x2, y2) in the slope formula:

m = (11400 - 10900) / (140 - 120)

m = 500 / 20

m = 25

Thus, the slope of the line is 25.

Finding the y-intercept (b):

Now we can find the y-intercept (i.e., the company's daily fixed costs) by substituting 25 for m and (120, 10900) for (q, C(q)) and in the slope-intercept form:

10900 = 120(25) + b

(10900 = 3000 + b) - 3000

7900 = b

Thus, the company's daily fixed costs are $7900.

User Efi G
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