Question

The dollar cost of producing x bagels is given by C(x) = 300 + 0.25x - 0.7(x/1000)^3. Determine the cost of producing 2000 bagels.

Answer 1

The cost of producing 2000 bagels, using the cost function C(x) = 300 + 0.25x - 0.7(x/1000)^3, is calculated to be $805.60.

Step-by-step explanation:

To determine the cost of producing 2000 bagels, we will plug x = 2000 into the provided cost function C(x) = 300 + 0.25x - 0.7(x/1000)^3. Following the order of operations, we first evaluate (2000/1000)^3, then multiply by 0.7, and after that incorporate the remaining terms.

Step by step calculation:

1. (2000/1000)^3 = (2)^3 = 8
2. -0.7 × 8 = -5.6
3. 300 + (0.25 × 2000) - (-5.6) = 300 + 500 + 5.6
4. Final cost C(2000) = 300 + 500 + 5.6 = $805.60

Therefore, the cost of producing 2000 bagels is $805.60.