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Cost Function Analysis for Bicycle Helmet Production Based on Assembly Line Hours

This example explores how to determine the cost of producing bicycle helmets in relation to the number of hours the assembly line is in operation. Given the production function n = P(t) = 0.75t - 2t^2, representing the number of helmets produced over t hours, and the cost function C(n) = 0.7n + 1000, which gives the cost based on the number of helmets, we show how to derive a cost function that depends on hours worked. We also find the production cost when the assembly line operates for 12 hours, providing a practical application of function composition.

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Cost Function Analysis for Bicycle Helmet Production Based on Assembly Line Hours

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  1. Composition of Functions

  2. Example 1 • Evaluate

  3. Your turn • Evaluate

  4. Example 4 • Find the indicated values for the following functions if:

  5. ENR Example 5 • The number of bicycle helmets produced in a factory each day is a function of the number of hours (t) the assembly line is in operation that day and is given by n = P(t) = 75t – 2t2. • The cost C of producing the helmets is a function of the number of helmets produced and is given by C(n) = 7n +1000. Determine a function that gives the cost of producing the helmets in terms of the number of hours the assembly line is functioning on a given day. Find the cost of the bicycle helmets produced on a day when the assembly line was functioning 12 hours.(solution on next slide)

  6. Solution to Example 5: • Determine a function that gives the cost of producing the helmets in terms of the number of hours the assembly line is functioning on a given day. • Find the cost of the bicycle helmets produced on a day when the assembly line was functioning 12 hours. ENR

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