### A company is planning to manufacture mountain bikes. The fixed monthly cost will be \$100,000 and it will cost \$100 to produce each bicycle.1. **A. Write the cost function, $ C $, of producing $ x $ mountain bikes per month.** \[ C(x) = \]2. **B. Write the average cost function, $ \bar{C} $, of producing $ x $ mountain bikes per month.** \[ \bar{C}(x) = \]3. **C. Find and interpret $ \bar{C}(500) $, $ \bar{C}(1000) $, $ \bar{C}(2000) $, and $ \bar{C}(4000) $.** - Interpret $ \bar{C}(500) $: \[ \bar{C}(500) = \] When 500 bicycles are produced in a month, it costs \$_____ to produce each bicycle. - Interpret $ \bar{C}(1000) $: \[ \bar{C}(1000) = \] When 1000 bicycles are produced in a month, it costs \$_____ to produce each bicycle. - Interpret $ \bar{C}(2000) $: \[ \bar{C}(2000) = \] When 2000 bicycles are produced in a month, it costs \$_____ to produce each bicycle. - Interpret $ \bar{C}(4000) $: \[ \bar{C}(4000) = \] When 4000 bicycles are produced in a month, it costs \$_____ to produce each bicycle. Click to select your answer(s). ### Cost Analysis for Manufacturing BicyclesA company is planning to manufacture mountain bikes. The fixed monthly cost will be \$100,000 and it will cost \$100 to produce each bicycle.#### Interpretation of Production Costs1. **Interpret $C(2000)$** - When \[ \square \] bicycles are produced in a month, it costs \$ \[ \square \] to produce each bicycle.2. **Interpret $C(4000)$** - When \[ \square \] bicycles are produced in a month, it costs \$ \[ \square \] to produce each bicycle.#### Horizontal Asymptote Analysis3. **Horizontal Asymptote of the Average Cost Function $C(x)$** - **Q**: What is the horizontal asymptote for the graph of the average cost function $C(x)$? (Type an equation) \[ \lim_{{x \to \infty}} C(x) = \[ \square \] \] - **Q**: Describe what this means in practical terms. - When \[ \square \] bicycles are produced in a month, the cost per bicycle approaches \$\[ \square \] as more bicycles are produced. - **Option A**: The cost per bicycle approaches \$100,000 as more bicycles are produced in a month. - **Option B**: When $ \[ \square \] $ bicycles are produced in a month, the cost per bicycle is at a minimum. - **Option C**: When $100,000$ bicycles are produced in a month, the cost per bicycle is at a minimum. - **Option D**: When $100,000$ bicycles are produced in a month, the cost per bicycle approaches \$100.#### Note:Based on the context, it seems most appropriate that the fixed costs dominate in the short production runs, and as more bicycles are produced, the average cost per bicycle should approach the variable cost of producing an additional bicycle, which is \$100. Therefore, the correct interpretation would likely lead to recognizing that as production increases, the average cost per bicycle stabilizes around the variable cost.

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A company is planning to manufacture mountain bikes. The fixed monthly cost will be $100,000 and it will cost $100 to produce each bicycle. A. Write the cost function, C, of producing x mountain bikes per month. C(x) =| B. Write the average cost function, C, of producing x mountain bikes per month. C(x) =D C. Find and interpret C(500), C(1000), C(2000), and C(4000).

A company is planning to manufacture mountain bikes. The fixed monthly cost will be $100,000 and it will cost $100 to produce each bicycle. A. Write the cost function, C, of producing x mountain bikes per month. C(x) =| B. Write the average cost function, C, of producing x mountain bikes per month. C(x) =D C. Find and interpret C(500), C(1000), C(2000), and C(4000).

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section: Chapter Questions

Problem 10QP

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