Question $2.(15$ pts$)$

Given the network in Figure $1,$ where the flow capacities along each branch are indicated: $($a$)$ Determine the maximum flow from source node $1$ to destination node $10,$ and identify the flow along each path. $($In this problem, please clearly indicate the path, and flow amount at each step$)$

$($b$)$ Formulate a linear programming model for this problem.

Question $3.(15$ pts$)$

The Donnor meat processing firm produces wieners from four ingredients: chicken, beef. pork, and a cereal additive. The firm produces three types of wieners: regular, beef, and all$-$meat. The company has the following amounts of each ingredient available on a daily basis as show in Table $1.$ Each type of wiener has certain ingredient specifications, as shown in Table $2.$ The firm wants to know how many pounds of wieners of each type to produce to maximize profits.

Formulate a linear programming model for this problem.

$\backslash$table$[[,$Pounds$/$Day$,$Cost$/$Pound$],[$Chicken$,200,50\mathrm{.}20],[$Beef$,300,50\mathrm{.}30],[$Pork$,150,50\mathrm{.}50],[$Cereal additive,$400,50\mathrm{.}05]]$

Cereal additive

Table $1$: Ingredients availability and cost.

Table $2$: Product specifications and price.