Using the precedence relationship and following the rules of network construction, the required network is shown in the following diagram

Using the precedence relationship and following the rules of network construction, the required network is shown in the following figure.

(i) Variables:
Let x₁ and x₂ represent the number of fans and sewing machines.
(ii) Objective functions:
Let Z be the profit of the dealer.
∴ Maximize Z = 22x₁ + 18x₂ is the objective function.
(iii) Constraints:
\({ x }_{ 1 }+{ x }_{ 2 }\le 20\)
\({ 360x }_{ 1 }+{ 240x }_{ 2 }\le 5760\)
(iv) Non-negative restrictions:
Since the number of fans and sewing machine cannot be negative, we have x₁, x₂ ≥ 0.
Hence, mathematical formulation of the LPP is
Maximize \(Z=22{ x }_{ 1 }+18{ x }_{ 2 }\)
Subject to the constraints
\({ x }_{ 1 }+{ x }_{ 2 }\le 20\)
\({ 360x }_{ 1 }+{ 240x }_{ 2 }\le 5760\)
and x₁, x₂ ≥ 0.

(i) Variables:
Let x₁, x₂ represents the first and second type of bonds respectively.
(ii) Objective function:
Let Z be the maximum return
\(\therefore \quad Z=\frac { 8 }{ 100 } { x }_{ 1 }+\frac { 10 }{ 100 } { x }_{ 2 } \Rightarrow Z=0.08{ x }_{ 1 }+0.1{ x }_{ 2 }\)
(iii) Constraints: 
\({ x }_{ 1 }+{ x }_{ 2 } \le 70,000\)
\({ x }_{ 1 } \ge 10,000\)
\( { x }_{ 2 } \le 30,000\)
(iv) Non-negative restrictions:
Since the number of first and second type of bonds cannot be negative,x₁, x₂ ≥ 0.
Hence, the mathematical formulation of the LPP is maximize \(Z=0.08{ x }_{ 1 }+0.1{ x }_{ 2 }\)
Subject to the constraints 
\({ x }_{ 1 }+{ x }_{ 2 } \le 70,000\)
\( { x }_{ 1 }\ge 10,000\)
\({ x }_{ 2 }\le 30,000\)
and x₁, x₂ ≥ 0.

(i) Variables: Let x₁be the executive class tickets and x₂ be the economy class ticket.
(ii) Objective function: Let Z be the maximum profit
Maximize Z=1000x₁+600x₂
(iii) Constraints:\({ x }_{ 1 }\ge 20\)
\(\Rightarrow { x }_{ 2 }\ge 4{ x }_{ 1 }\ and\ { x }_{ 1 }+{ x }_{ 2 }\le 200\)
\( \Rightarrow 4{ x }_{ 1 }\le { x }_{ 2}\ and\ { x }_{ 1 }+{ x }_{ 2 }\le 200\)
\(\Rightarrow 4{ x }_{ 1 }-{ x }_{ 2 }\le 0 \ and \ { x }_{ 1 }+{ x }_{ 2 }\le 200\)
(iv) Non-negative restrictions:
Since the number of tickets cannot be negative, \({ x }_{ 1 },{ x }_{ 2 }\ge 0\)
Hence, the mathematical formulation of the LPP is Maximize Z=1000x₁+600x₂
Subject to the constraints
\({ x }_{ 1 }+{ x }_{ 2 } \le 2000\)
\( { x }_{ 1 } \ge 20\)
\(4{ x }_{ 1 }-{ x }_{ 2 } \le 0 \ and \ { x }_{ 1 },{ x }_{ 2 }\ge 0\)

The required network for the above information.

Using the precedence relationships and following the rules of network construction, the required network is shown in following figure.

Using the precedence relationships and following the rules of network construction, the required network diagram is shown in following figure.