By R. H. Mole

Ebook through Mole, Richard H.

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Notice that the output produces a warning if the value of the controlled variable hes outside the range of the original data which was used to obtain the line of best fit. This class of estimate is known as extrapolation, and it has much less reliability than an interpolated estimate, since there can be n o assurance that the linear relationship holds for arbitrarily small or large volumes. 2. H e r e the controlled variable is the time period and so a convenient choice is a quarterly variable with values from 1 to 14, T h e d e p e n d e n t variable C is not cost, but sales.

_i(V/_i - V/) + NVi or C = Co + c,(N - no) + C2ÍN - n,) -l· , . 4 for the case of a 2-piece linear relationship ( i . e . L = 2 ) . S. = L Σ 7=1 j where the first s u m m a t i o n extends over the Λ^Λ^ observations. S. with respect to C(), Ci, C2, . . , C/^ o n e finds the following L + 1 Unear equations in Co, c,, C 2 , . . ^U for / = 1, 2, . . , L . = ¿ w h e r e c = ( c o , ci, C2, . , and = IC/(iV/ - for / = 1, 2, . . , L 7 = 1, 2, . . , L . T h u s A is symmetric and this fact allows the use of a simplified m e t h o d of solution (Gaussian elimination for a symmetric matrix of coefficients).

T a b l e 70 PROCinput_revenue 80 P R O C p r i n t _ t a b l e 9 0 END 100 1000 DEFPROCinput_costs 1 0 1 0 INPUT "MAXIMUM VOLUME " , N N 1 0 2 0 INPUT "MAX NO OF COST ELEMENTS",EMAX :Z$="C" 1 0 3 0 REPEAT 1 0 4 0 E=E+1 1 0 5 0 PRINT "COST ELEMENT " ; E 1 0 6 0 INPUT "NO OF LINEAR SEGMENTS " , L 1 0 7 0 INPUT "FIXED COST " , F 1 0 8 0 PRINT "MARG. KNOTS" 1 0 9 0 PRINT "COST" 1 1 0 0 PRINT " V " , " N " 1 1 1 0 FOR 1 = 1 TO L 1 1 2 0 INPUT V 1 1 3 0 IF K L INPUT T A B ( 1 0 ) , N ELSE N=NN 1 1 4 0 I F E = l THEN ν ( I ) = V : n ( I ) = N 1 1 5 0 IF E>1 THEN P R 0 C s t e p 2 1 1 6 0 NEXT I 1 1 7 0 IF E = l THEN 1=L : f = F 1 1 8 0 UNTIL E=EMAX 1 1 9 0 PRINT 1 2 0 0 ENDPROC 1210 2 0 0 0 DEF P R 0 C s t e p 2 2 0 1 0 IF 1 = 1 THEN f = f + F : j = l 2020 n ( 0 ) = 0 2030 i=0 2 0 5 0 REPEAT 2060 i = i + l 2 0 7 0 UNTIL N > = n ( I - l ) + l AND N < = n ( i ) 2 0 8 0 I F N < n ( i ) THEN P R O C s t e p l 2 0 9 0 REPEAT 2100 v ( j ) = v ( j ) + V 2110 j=j+l 2 1 2 0 UNTIL j = i + l 2 1 3 0 ENDPROC 2140 3 0 0 0 DEF P R O C s t e p l 3 0 1 0 FOR k = l + l TO i + 1 STEP - 1 3020 v ( k ) = v ( k - l ) 3030 n ( k ) = n ( k - l ) 3 0 4 0 NEXT k 3050 n ( i ) = N 3060 1=1+1 3 0 7 0 ENDPROC 3080 4 0 0 0 DEF P R O C p r i n t .