11
MVPs
w¡ 11
for each input,
yield the optimal
MVP = P .
XI XI
MVPx2 = Px2
Thus the simultaneous solution of equation (2-2)
levels of the X¡ through Xn inputs.
(2-2)
Linear programming does not allow for the estimation of the mar
ginal 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 ex
hausted 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 are 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 prob
abilities, decision makers then may be able to compensate or allow
for risk.