Problem: Let R(q) = 1/100 x^2 be a revenue function and C(q) = sqrt(x) be a cost function for a particular business commodity.
a) Demonstrate that C(q) = R(q) at approximately q =21.544.
b) Determine the marginal cost and marginal revenue functions.
c) Suppose the supply and demand for this commodity equalize at q=25. Determine the profit from this quantity of production.
d) Is the business justified in producing a 26th item based on the analysis of marginal cost and revenue? Explain.