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.
