Question

A military commander has been assigned the task of defending an asset from enemy air attack. There are two types of air defence missiles and 5 missiles of each type are available for deployment. The installation cost is 7 units for each type-A missile and 8.5 units for each type-B missile. The total budget available is 60 units. Each type-A missile requires 6 persons for handling, whereas each type-B missile can be handled by 2 persons. There are only 32 trained persons to handle the missiles at the site. If the site is not defended, the enemy aircraft are estimated to destroy 95% of the asset value. However, they are able to destroy 82% of the asset value in the presence of one type-A missile and 86% of asset value in presence of one type-B missile. Determine the mix of missiles that provides maximum protection to the asset against an attack of enemy aircraft aiming simultaneously.

Answer 1

Observe that we can take the respective cost and man power in a table which will help us to come up with constraints. The table is given below:

	A	B	Total
Number	x	y
Cost	7	8.5	60
Person	6	2	32
Prevention of Damage	95-82=13	95-86=9

Hence our Objective Function and the Constraints are the following:

This will lead to a bounded region with the following corner points and corresponding value of objective equation:

Corner Points	Objective
(0,0)	0
(0,5)	45
(2.5,5)	77.5
(4.11,3.68)	86.55
(5,1)	74
(5,0)	65

hence, as we need an integer solution, the best solution would be 4 type A missile and 3 type B missile.