Chapter 4 - Applications of Linear Systems and Matrices

Section 4.5 -  An Application of Matrix Multiplication to Economics

Example 4.5.1

(T1Headings={{"labor per vehicle","compact car","sedan","sports car","truck","SUV"},{"upholstery",.735,1.105,.825,.765,.855},{"metal",1.515,1.785,1.325,1.605,1.905},{"electrical",1.105,1.325,.905,1.535,1.725},{"general assembly",2.465,2.535,2.015,2.935,3.265}})//MatrixForm

(P1Headings={{"vehicle per month","January","February","March"},{"compact car",7825,8635,8950},{"sedan",5085,5530,5815},{"sports car",1205,1365,1420},{"truck",4095,5140,5375},{"SUV",3820,4235,4680}})//MatrixForm

(M1=Drop[T1Headings,1,1].Drop[P1Headings,1,1])//MatrixForm

(M1Headings=Join[{{"labor per month"},{"upholstery"},{"metal"},{"electrical"},{"general assembly"}},Join[{{"January","February","March"}},M1],2])//MatrixForm

(People1=Ceiling[1/8 M1])//MatrixForm

(People1Headings=Join[{{"people per month"},{"upholsterers"},{"metal workers"},{"electrical workers"},{"general assembly workers"}},Join[{{"January","February","March"}},People1],2])//MatrixForm

0.9375 1.0415

1-0.97640625

(T2=.9375 Drop[T1Headings,1,1])//MatrixForm

(P2=1.0415 Drop[P1Headings,1,1])//MatrixForm

(M2=T2.P2)//MatrixForm

0.97640625 M1//MatrixForm

(People2=Ceiling[1/8 M2])//MatrixForm

(People1Headings=Join[{{"people per month"},{"upholsterers"},{"metal workers"},{"electrical workers"},{"general assembly workers"}},Join[{{"April","May","June"}},People2],2])//MatrixForm

D1={{.00825,.0115,.00615,.00905,.0125},{.015,.01785,.01125,.01905,.01815},{.00735,.00775,.00615,.00845,.00875},{.0165,.01875,.01415,.01925,.01965}};

Ceiling[D1.Drop[P1Headings,1,1]]//MatrixForm

R1={{7.85,15.10,9.15,35.20},{10.25,18.90,11.25,42.70},{8.15,15.75,9.45,29.65},{13.95,21.05,11.80,51.75},{14.35,20.60,10.95,48.15}};

(Costs1=Ceiling[R1.D1.Drop[P1Headings,1,1]])//MatrixForm

(Costs1Headings=Join[{{"type of vehicle per month"},{"compact car"},{"sedan"},{"sports car"},{"truck"},{"SUV"}},Join[{{"January","February","March"}},Costs1],2])//MatrixForm

Total[Drop[Costs1Headings,1,1],2]