Find the price elasticity of demand for the demand function x = 10 – p where x is the demand and p i the price. Examine whether the demand is elastic, inelastic or unit elastic at p = 6.

Find the interval in which the function f(x) = x² – 4x + 6 is strictly increasing and strictly decreasing.

Given C(x) = \(\frac { { x }^{ 3 } }{ 6 } \)5x + 200 and p(x) = 40 – x are the cost price and selling price when x units of commodity are produced. Find the level of the production that maximize the profit.

The average cost function associated with producing and marketing x units of an item is given by AC = 2x - 11+\(\frac { 50 }{ x } \). Find the range of values of the output x, for which AC is increasing.

A manufacturing company has a contract to supply 4000 units of an item per year at uniform rate. The storage cost per unit per year amounts to Rs. 50 and the set up cost per production run is Rs. 160. If the production run can be started instantaneously and shortages are not permitted, determine the number of units which should be produced per run to minimize the total cost.