Marginal Cost Questions

A toy manufacturing firm has its variable cost $C(x)={\alpha }^{2}x(\beta \sqrt{x}+\alpha \beta )$, where $x$ is the number of toys produced. The cost of storage and other fixed expenses are $Rs.4500$. If the marginal cost is $40$ when $144$ toys have been produced and $\alpha \beta =1$, find the possible values of $\alpha$.

A manufacturing firm has its variable cost given by $C(x)=x(12-x^3)$. The price per unit is $p(x)=6x-2$. Find the marginal revenue when $3$ units were in demand.

A company has a variable cost $V(x)=3x^2+3500$ and a fixed cost of $₹2000$. The marginal cost of producing $50$ units is: