a$)$ Define the following terms in relation to input $-$ output analysis;

i$)$ Technical coefficients.

ii$)$ Intermediate demand.

iii$)$ Close input$-$output model.

b$)$ Name any two assumptions of input $-$ output analysis.

c$)$ Technological matrix for a two sector economy is given by

$T=\left[\begin{array}{ccc}\text{:}& A& B\\ A& 0\mathrm{.}4& 0\mathrm{.}2\\ B& 0\mathrm{.}5& 0\mathrm{.}4\end{array}\right]$ The final demand forecast is approximately Sh$.60$ million

for sector A and Sh$.90$ million for sector B$.$ Calculate the total worth of primary

inputs.

d$)$ Minimize: $z=3x^2-50x+6xy+3y^2-30y+102$

Subject to: $x+3y=18$