Chapter 4 - Applications of Linear Systems and Matrices

Section 4.3 -  Applications of Linear Systems to Economics

Example 4.3.1

EqnFed=x==0.193 (57650-y-z-w);

EqnState=y==0.0425 (57650-x-z-w);

EqnCity=z==0.0055 (57650-x-y-w);

EqnProp=w==0.0235 (57650-x-y-z);

SolnRates=Solve[{EqnFed,EqnState,EqnCity,EqnProp},{x,y,z,w}]

FedRate=(x/.SolnRates[[1]])/57650

StateRate=(y/.SolnRates[[1]])/57650

CityRate=(z/.SolnRates[[1]])/57650

PropRate=(w/.SolnRates[[1]])/57650

OverAllRate=FedRate+StateRate+CityRate+PropRate

Example 4.3.2

EqnTotal=x+y+z==248000;

EqnYield=0.0435 x+0.0615 y+0.0875 z==19500;

EqnTriple=z==3 (x+y);

Solve[{EqnTotal,EqnYield,EqnTriple},{x,y,z}]

Example 4.3.3

Soln = Solve[{c-(.01 c+.03 g+.11 s+.10 e)==18000000,g-(.05 c+.01 g+.15 s+.23 e)==74000000,s-(.08 c+.06 g+.02 s+.05 e)==51000000,e-(.17 c+.14 g+.09 s+.03 e)==106000000},{c,e,g,s}]

(c-18000000)/.Soln[[1]]

(e-106000000)/.Soln[[1]]

(g-74000000)/.Soln[[1]]

(s-51000000)/.Soln[[1]]