Question

An airline agrees to charter planes for a group. The group needs at least 160 first class seats and at least 300 tourist class seats. The airline must use at least two of its model 314 planes which have 20 first class and 30 tourist class seats. The airline will also use some of its model 535 planes which have 20 first class seats and 60 tourist class seats. Each flight of a model 314 plane costs the company Rs 100,000 and each flight of a model 535 plane costs Rs 150,000. How many of each type of plane should be used to minimize the flight cost? Formulate this as a LPP.

Answer 1

Let x number of model 314 planes and y  number of model 535 planes were used.

It is given that cost of one model 314 plane is Rs 100000 and cost of one model 535 plane is Rs 150000.
Therefore, cost of x model 314 plane is Rs 100000x and cost of y model 535 plane is Rs 150000y.

Total cost price = 100000x + 150000y

​​Let Z denote the total cost

Then, Z = 100000x + 150000y

Also, 
Each model 314 planes have 20 first class and 30 tourist class seats and each model 535 planes has 20 first class and 60 tourist class seats.The group needs 160 first class seats and 300 tourist class seats.
The group needs 160 first class seats and 300 tourist class seats.

\[\therefore 20x + 20y \geq 160\]
\[ 30x + 60y \geq 300\]

Number of planes cannot be negative.
Therefore, 

\[x, y \geq 0\]

Hence, the required LPP is as follows:
Min Z = 100000x + 150000y 

subject to 

\[20x + 20y \geq 160\]

\[ 30x + 60y \geq 300\]

\[x \geq 0, y \geq 0\]