Business Management—Cost Analysis: The Seas Beginning Company determines that the cost of producing their Deluge Buster rain coat is given by the cost function
C(x) = 1000 + 35x − 0.01x2 0 ≤ x ≤ 300
where x represents the number of raincoats produced each day, and C(x) represents the cost in dollars.
(a) Determine the average rate of change in cost as daily production increases from 100 to 150 coats per day.
(b) Approximate the instantaneous rate of change in cost at a production level of 200 coats a day.
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