79.

1. $\{\begin{array}{lllll}a& =& 0.1b& +& 1000\\ b& =& 0.2a& +& 780\end{array}$

2. $\left[\begin{array}{rrr}1& -0.1& 1000\\ -0.2& 1& 780\end{array}\right]$

3. $a=1100,b=1000$

81.

1. $\{\begin{array}{rcl}l& =& 0.4t+0.2f+10\text{,}000\\ t& =& 0.5l+0.3t+20\text{,}000\\ f& =& 0.5l+0.05t+0.35f+10\text{,}000\end{array}$

2. $\left[\begin{array}{rrrr}1& -0.4& -0.2& 10\text{,}000\\ -0.5& 0.7& 0& 20\text{,}000\\ -0.5& -0.05& 0.65& 10\text{,}000\end{array}\right]$

3. food, $55,000; transportation, $61,000; labor, $45,400

83. $T_1=110,T_2=140,T_3=60$

85.

1. $\{\begin{array}{rrrrrrr}x& -& y& & & =& 70\\ -x& +& & & z& =& -120\\ & & y& -& z& =& 50\end{array}$

2. $\{(120+z,50+z,z)\}:0\le z\le 130$

87. $y=2x^2-3x+4$

89. $f(x)=1-{\displaystyle \frac{3\sqrt{2}}{2}}\text{ sin }(x)-{\displaystyle \frac{5}{2}}\text{ sin }(2x)$

91. $y=-x^3+2x^2+3x+1$

93. $f(x)=\{\begin{array}{l}{\displaystyle \frac{2}{3}}x+{\displaystyle \frac{4}{3}},1\le x\le 4\\ -{\displaystyle \frac{3}{2}}x+10,4\le x\le 6\end{array}$