Utility Maximization Subject to Multiple Constraints

Applying method of Lagrange multipliers, an attempt has been made to derive mathematical formulation to workout optimal purchasing policy in order to maximize utility of an individual consumer subject to multiple constraints; in this particular illustration, two constraints: 1) budget constraint, and 2) coupon constraint. An explicit example is given in order to examine the behaviour of an individual consumer and to support the analytical arguments, using comparative static analysis.