The cost function for a product in a firm is given by $5q^2$, where $q$ is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

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5. Profit is $P(q)=50q-5q^2$. Maximizing this quadratic by differentiation gives $P'(q)=50-10q=0\Rightarrow q=5$. Since $P''(q)=-10<0$, this is a maximum.

The cost function for a product in a firm is given by \(5q^2\), where \(q\) is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

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