  Breakability rate of fragile item depends on the accumulated stress of heaped
stock level. So breakablility rate can be considered as dependent parameter of
stock variable. The unit production cost is a function of production rate and
also dependent on raw material cost, development cost and wear-tear cost. The
holding cost is assumed to be non-linear, dependent on time. Here optimal
control problem for a fragile item under finite time horizon is considered. The
profit function which consists of revenue, production and holding costs is
formulated as a Fixed-Final Time and Fixed State System(cf. Naidu (2000))
optimal control problem with finite time horizon. Here production rate is
unknown and considered as a control variable and stock level is taken as a
state variable. It is formulated to optimize the production rate so that total
profit is maximum. As particular cases, models are evaluated with and without
breakability. The models are solved by using conventional Variational Principle
along with the non-linear optimization technique-Generalised Reduced Gradient
Method (LINGO 12.0). The optimum results are illustrated both numerically and
graphically. Some sensitivity analysis on breakability coefficient are
presented.
