1. 
    1. $x_1,x_2>0$
    2. It is always feasible
    3. $x_1\leq 0 \vee x_2\leq 0$
2. Let $i$ be the type of meat: Ham=1,Bellies=2,Picnics=3. Let $j$ be the method of preparation: 1=Fresh, 2=Smoked on regular time, 3=Smoked on overtime. Let $p_{ij}$ be the net profit om meat type $i$ and method $j$. Let $x_{ij}$ be the amount of meat $i$ should be prepared with method $j$. Let $M_i$ be the amount of meat $i$: $M_1=480,M_2=400,M_3=230$. Let $N_j$ be the amount of meat that can be prepared with method $j$: $N_1=\infty,N_2=420,N_3=250$. Now we get the following LP:$$\begin{aligned}\text{maximize}&\sum_{i=1}^3\sum_{j=1}^3p_{ij}x_{ij}\\\text{subject to}&\sum_{j=1}^3x_{ij}\leq M_i \forall i\in\{1,2,3\}\\&\sum_{i=1}^3x_{ij}\leq N_j\forall j\in \{1,2,3\}\end{aligned}$$<font color="red">Add:</font>$$x_{ij}\geq 0\forall i,j\in \{1,2,3\}$$
3. In these questions $x_i=1$ denotes that investment $i$ is chosen and $x_i=0$ denotes that it is not chosen.
    1. $\sum_{i=1}^7 x_i\geq 1$
    2. $\sum_{i=1}^7x_i<7$
4. We will give the steps of the simplex method here
    0. The three slack variables are the same as in the slides. 
    1. $(x,y)=0$.
    2. Fix $y=0$ and increase $x$. We see that $x\leq 16,9,8$ , so $(x,y)=(8,0)$.
	3. Replace all $x$ by $8-\frac{2}{3}y-\frac{1}{3}s_3$ and we get $$\begin{aligned}\text{maximize  } &  320-13\frac{1}{3}S_3+3\frac{1}{3}y\\\text{subject to }&-\frac{1}{3}s_3+1\frac{1}{3}y\leq 8\\&-\frac{1}{3}s_3+\frac{1}{3}y\leq 1\\&\frac{s_3}{3}+\frac{2}{3}y\leq 8.\end{aligned}$$
	4. Now we keep $s_3=0$ constant and increase $y$ as much as possible.  The maximum for $y$ is $3$. Now we see that that because $s_3=0$, that $x=6$.