MVPs- for each input. Thus the simultaneous solution of equation (2-2) will yield the optimal levels of the Xi through X n inputs.
MVP xi Pxi MVPx2 P x2
(2-2)
MVPxn Pxn
Linear programming does not allow for the estimation of the marginal value of an input while all other inputs are held constant. Rather, the shadow prices which are given by the program indicate the increase in profit (when the objective function is a profit function) if the supply of the scarce resource is increased by one unit. A scarce resource is one for which the supply has been completely exhausted in the program solution. The shadow price represents the monetary value of the increase in output using the additional unit of the scarce input in combination with the corresponding quantities of the other inputs.
Risk and Uncertainty
The distinction between risk and uncertainty is that the former can be quantified in terms of probabilities. The probabilities of outcomes or occurrences in a risk situation dre measurable; whereas, in the case of uncertainty they cannot be meaningfully measured (20, pp. 19-21, 197-233). When outcomes can be expressed in terms of probabilities, decision makers then may be able to compensate or allow for risk.