Real-World Applicationshard
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A tech startup projects quarterly revenue using the model R(q)=50q2q2+0.1q3R(q) = 50q - 2q^2 + 0.1q^3 thousand dollars, where qq is the quarter number. Operating costs are C(q)=10+3q+0.05q2C(q) = 10 + 3q + 0.05q^2 thousand dollars. Profit is P(q)=R(q)C(q)P(q) = R(q) - C(q). After how many quarters is the marginal profit (rate of change of profit) equal to zero?