) A company determines that its marginal revenue per day is given by R'(t) = 100et , R(0) = 0, where R(t) = the revenue, in dollars, on the tth day. The company's marginal cost per day is given by C'(t) = 140 - 0.3t, C(0) = 0, where C(t) = the cost, in dollars, on the tth day. Find the total profit from t = 0 to t = 5 (the first 5 days). Round to the nearest dollar. Note: P(T) = R(T) - C(T) = T 0 ∫ [R'(t) - C'(t)] dt.

The answer is below

Explanation:

The marginal revenue R'(t) = and the marginal cost C'(t) = 140 - 0.3t.

The total profit is the difference between the total revenue and total cost of a product, it is given by:

Profit = Revenue - Cost

P(T) = R(T) - C(T)

P(T) = ∫ R'(T) - C'(T)

Hence the total profit from 0 to 5 days is given as

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