Energy Systems Analysis for Developing Countries
The lecture notes presented in these pages were originally developed for use in the Energy Management Training Program (EMTP), sponsored by the Office of Energy, U. S. Agency for International Development. This program, held at Brookhaven National Laborat
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S.lect,on M"II,ple
Network
~nll"'.
Reg"",on. Inl.rclep.ndenci lilli, 181 pag.. 1074
end Opt"".'
Vol 10. 5 I'",'no. A N.cHe Struc;l"" of Incr:>rM Di'ln~ IX. 13& pIIlII. 11118.
Vol, 117: ()piimoz'loon ,rod ()per.1ooM R_,eII. ProoHd'nglI1I7& . Edited by W . OIIIIi ,rod It R;a.,. IV. 3UI ~ 11178. Vol. 118: T"fflc Equrlibnum MeIhodI. Proceed'ng' 11174. Ed,1Id by 101. A. FIori,n. XXlIl 4 32 pIIlII. 11178. Val. 1111: 1,,",1Ion in Small Countr-. PrIlCllld,ng. 11174 EdiIed by H. hid!. VI, 3158 PIIQII. 11171. Vol. 120: G. ~mp.. Sp.ctllC.ltron .rod Elb ..... tron 01 MultipleOutput P>oduction Functoon,. VI. 1111 """,. 11178. On R""",,"_ Proc:._ ,n a--.g Val. 121: J. W.
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Vol. 130: Mwh,pIe C" ..... DlcrIlOll M.lung, Joup·.,.Jo. . .. F....... PrIi"lt". VI, 282 1(1".
Vol. 122: 101. 5 . Satar... lAd C. M. sn.a,..Foundlotron. of Opctmot'loon VI. 1113 PIIQII. !1I711
Vol. 1110: Sa_II". Supercrlbcal Wi"" SocIoon. 111. VI, 17V pIIlII. 11117.
Vol. 123: Muhopll 0","" DIaIion M.k,ng. K)'OIO 1117!!i. EdrIICI by M. Zeleny. XXVII. 3 4 !!i pegM. 11178.
'obi. l!!i l: C. A. &: ...........8. "'-"ory-Produclion Theory. VI, 1II PIIIl'I.
Vol. 1' 4 : 101. J. Todd. T'-Compwlionof Fi,ed Poonla.rod~· bone. VII, 1211 PIIQII. tV78.
Vol. 1112: KOlICh . . .1. Notwrtnd'\t4' OpIo ....Immung ....... koIlIngOr'Iellg.... Slandot18 bIo I/IQIbIrrIr Nacfth"" VI,
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Vol. 128 : 1'*9If Progr'lI'Wnrng .nd R"'1ed At .... A ctu,ilied Bibliogr. P"J. Ediled by c.1T W(Y -
Xf3)
differentiation with respect to
B,
and setting equal to zero, yields
hence
clearly, If all wi = 1, then W Is the identity matrix, and XTW unweighted regression.
39
xTr
X ~ which
Is the result fo
2.3
LINEAR PROGRAMMING16 Linear programming can best be introduced by example.
Consider some
hypothetical country, which we shall call Republica,17 which produces only two
goods-agricultural
goods,
Xl
and
machinery,
x2.
Assume
that
three
primary inputs are available--labor, energy and capital, and that to produce one unit of xl and x2, the following inputs are required. Output Input
xl
x2
10
5
Capital
2
5
Energy
2
4
Labor
Suppose both units of Xl and X2 have the same value, and that the planners in Republica wish to maximize total output in the economy, i.e. (2.64) Suppose also that the total supply of labor is 25, of capital is 15 and of energy is 10 units.
What is the optimum combination of production in Repub-
lica? Obviously, production is contrained by resources; from the above table it follows that 10xi + 5x2 2Xl + 5x2 2xl + 4x2
i
25
< 15 < 10
(2.65)
Xl and x2
