Question

A military commander has been assigned the task of defending an asset from enemy air attack. Commander has two types of air defense missiles; 5 missiles each of type I and type II are available for deployment. Each type I missile costs 7 units for installation and each type II missile costs 8.5 units for installation. The total budget available is 60 units. Each type I missile requires 6 persons for handling whereas each type II requires 2 persons. There are only 32 trained persons to handle the missiles at the site. If the site is not defended the enemy aircrafts are estimated to destroy 95% of the asset value. If one type I missile is deployed on the site, it is expected to save 13% of the asset value. Similarly, deployment of one type II missile is estimated to save 9% of the asset value. In other words, the enemy aircrafts which were earlier capable of destroying 95% of the asset value are able to destroy 82% of the asset value in the presence of one missile of type I and 86% of the asset value in the presence of one missile of type II. Formulate an LP to determine the mix of missiles that provides maximum protection to the asset against an attack of enemy aircrafts aiming simultaneously.

Answer 1

Explanation:

we have A and B

for A,

95-82 = 13

for B,

95-86 = 9

cost of A = 9

cost of B = 8.5

total = 60

for person

A = 6,

B = 2

Total = 32

setting up objective function:

13x + 9y

constraints:

0≤x≤5, 0≤x≤5

7x + 8.5y ≤ 60

6x + 2y ≤ 32 this can be reduced by 2

3x + y≤16

this would take us to a bounded region which has the corner points and the objective values in the attachment i added.