The objective function maximize the profit

A private airlines company is considering purchase of three types of jet passenger planes so as to improve their passenger service. The 100-seater planes costs Rs.50 crores each; the 50-seater planes costs Rs.30 crores each and the 20-seater planes costs Rs.10 crores each. The company has budgeted Rs.800 crores for the purchase of these planes in the next financial year. The three types of planes, if purchased would be utilized at effectively the maximum capacity. The Finance Department estimates the net annual profit resulting from utilization of these planes as Rs.8 crores each for the 100-seaters, Rs.5 crores for the 50-seaters and Rs.2 crores for the 20-seater planes. The HRD estimates that 20 trained pilots will be available, and if only 100-seater planes were purchased then the maintenance facilities would be able to handle 15 new planes. However, each 100-seater plane is equivalent to 1.2 of 50-seater planes and each 100-seater plane is equivalent to 1.8 of 20-seater planes in terms of their use in maintenance facilities. Formulate the problem to improve the company’s performance.

Let be the number of 20-seater plane, be the number of 50-seater planes and be the number of 100-seater planes. So, from the data given, we form a table as shown below.

Jet planes	Profit (Crores)	Cost (crores)
20-seater	2	10
50-seater	3	30
100-seater	5	50
Total		800

Maintenance capacity constraints,

Using the above constraints we can formulate the problem to improve the performance of the company. The Objective function is to maximize the profit.