Mathematics

Mathematics

Problem

For a particular item, total cost and total revenue (in dollars) are modeled by C(q)=0.005q3+4q+2500andR(q)=50q,C(q)=0.005q^{3}+4q+2500 \quad\text{and}\quad R(q)=50q, where qq is the number of units produced and sold. Determine the production level qq (to the nearest whole unit) at which the profit ceases to increase and begins to decrease.

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