年份 1970 1972 1974 1976 1978 1980 年增长率（%） 0.87 0.85 0.89 0.91 0.95 1.10 为了从1.3表2估计1980年的人口，仍用上面的记号，人口增长率满足微分方程
dx?r(t)x(t),它在初始条件x(0)?x0下的解为 dtt0 x(t)?x0e?r(u)du
因为在题目中增长率r(u)以离散型数据给出（表3），所以上式要用数值积分计算.用梯形公式计算的结果是，1980年该地区人口为230.2（百万）.
%p96 renkou(2) clc,clear y(1)=210
r=[0.87 0.85 0.89 0.91 0.95 1.10]*0.01； t=0:2:10； for i=2:6
y(i)=y(1)*exp(2*trapz(r(1:i))); end y' 或者
%p96 renkou(2) clc,clear
y(1)=210
r=[0.87 0.85 0.89 0.91 0.95 1.10]*0.01 t=0:2:10 for i=2:6
y(i)=y(1)*exp(trapz(t(1:i),r(1:i))); end y'
第七次 第四章Lingo练习
程序1： max 72x1+64x2 st
2) x1+x2<50
3) 12x1+8x2<480 4) 3x1<100 End
max 72x1+64x2 st
2) x1+x2<50
3) 12x1+8x2<480 4) 3x1<100 end
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 3360.000
VARIABLE VALUE REDUCED COST X1 20.000000 0.000000 X2 30.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 48.000000 3) 0.000000 2.000000 4) 40.000000 0.000000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 72.000000 24.000000 8.000000 X2 64.000000 8.000000 16.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 50.000000 10.000000 6.666667 3 480.000000 53.333332 80.000000 4 100.000000 INFINITY 40.000000 程序2：max 24x1+16x2+44x3+32x4-3x5-3x6 s.t.
2) 4x1+3x2+4x5+3x6<600 3) 4x1+2x2+6x5+4x6<480 4) x1+x5<100 5) x3-0.8x5=0 6) x4-0.75x6=0 End
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 3460.800
VARIABLE VALUE REDUCED COST X1 0.000000 1.680000 X2 168.000000 0.000000 X3 19.200001 0.000000 X4 0.000000 0.000000 X5 24.000000 0.000000 X6 0.000000 1.520000
ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 3.160000 3) 0.000000 3.260000 4) 76.000000 0.000000 5) 0.000000 44.000000 6) 0.000000 32.000000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 24.000000 1.680000 INFINITY X2 16.000000 8.150000 2.100000 X3 44.000000 19.750002 3.166667 X4 32.000000 2.026667 INFINITY X5 -3.000000 15.800000 2.533334 X6 -3.000000 1.520000 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 600.000000 120.000000 280.000000 3 480.000000 253.333328 80.000000 4 100.000000 INFINITY 76.000000 5 0.000000 INFINITY 19.200001 6 0.000000 INFINITY 0.000000 程序3：max 2x1+3x2+4x3 s.t.
2) 1.5x1+3x2+5x3<600
3) 280x1+250x2+400x3<60000 End
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 632.2581
VARIABLE VALUE REDUCED COST X1 64.516129 0.000000 X2 167.741928 0.000000 X3 0.000000 0.946237
ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.731183 3) 0.000000 0.003226
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 2.000000 1.360000 0.500000 X2 3.000000 1.000000 0.550000 X3 4.000000 0.946237 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 600.000000 119.999992 278.571411 3 60000.000000 52000.000000 10000.000000 程序4：max 2x1+3x2+4x3 st
2) 1.5x1+3x2+5x3<600
3) 280x1+250x2+400x3<60000 end gin3
LP OPTIMUM FOUND AT STEP 0