The total cost function for a product is C(x) = 850 ln(x + 10) + 1700 where x is the number of units produced. (a) Find the total cost of producing 200 units. (Round your answer to the nearest cent.) $ (b) Producing how many units will give total costs of $9500? (Round your answer to the nearest whole number.) units

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The total cost function for a product is C(x) = 850 ln(x + 10) + 1700 where x is the number of units produced. (a) Find the total cost of producing 200 units. (Round your answer to the nearest cent.) $ (b) Producing how many units will give total costs of $9500? (Round your answer to the nearest whole number.) units

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amcool amcool · Answer 1 · 2025-04-09T21:04:48-04:00

Answer:

a. $6,245.04

b. 9,605 units

Explanation:

(a) Find the total cost of producing 200 units. (Round your answer to the nearest cent.)

Given C(x) = 850 ln(x + 10) + 1700 ............................... (1)

Since x = 200 units, we substitute it into equation (1) solve as follows:

C(200) = 850 ln(200 + 10) + 1700

= 850 ln(210) + 1700

= 850(5.34710753071747) + 1700

= 4,545.04140110985 + 1700

C(200) = $6,245.04

Therefore, the total cost of producing 200 units is $6,245.04.

(b) Producing how many units will give total costs of $9500? (Round your answer to the nearest whole number.) units

To do this, we simple equate equation (1) to $9500 and solve for x as follows:

850 ln(x + 10) + 1700 = 9500

850lnx + In10 = 9500 - 1700

850lnx + 2.30 = 7,800

850lnx = 7,800 - 2.30

850lnx = 7,797.70

lnx = 7,797.70 ÷ 850

lnx = 9.17

x = e^9.17

x = 9,605

Therefore, 9,605 units will give total costs of $9500.