optimization

Consider the set S of points (x, y) ∈ R² which minimize the real valued function f(x, y) = (x + y − 1)² + (x + y)² Which of the following statements is true about the set S?

The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1 and PG2 are given as F1(PG1) = 0.1aP^2_G1 + 40 PG1 + 120 Rs/hour 0...

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by Plant 1 : C 1 = 350 + 6P 1 + 0.004P$$_1^2$$ Plant 2 : C 2 = 450 + aP 2 + 0.003P$$_2^2$$ wher...

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are $$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$ The...

The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in $$Rs/MWh$$ along with the generation limits for the two units are given belo...

If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant of the matrix is ____________.

The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${P_1}$$ and $${P_2}$$ in $$MW,$$ and are given by $$${{d{C_1}...

A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defi...

Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are $${\rm I}{C_1} = 20 + 0.3\,\,{P_1},\,{\rm I}{C_2} = 30 + 0.4\,\,{P_2},\...

A power system has two generators with the following cost curves Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour) Gene...

The incremental cost characteristic of two generators delivering $$200$$ $$MW$$ are as follows $$\,\,\,{{d{F_1}} \over {d{P_1}}} = 20 + 0.1{P_1},\,\,{{d{F_2}} \over {d{P_2}}} = 16...

In a power system, the fuel inputs per hour of plants $$1$$ and $$2$$ are given as $${F_1} = 0.20\,P_1^2 + 30\,{P_1} + 100\,\,$$ Rs per hour $${F_2} = 0.25\,P_2^2 + 40\,{P_2} + 150...