The commander of a battlefront11 must plan how to employ his f frontline and r reserve firepower to minimize the advance achieved over days t = 1,

c, 14 by an attack of opposing forces with firepower

a. Intelligence and battle simulations predict that each surviving unit of firepower in the attacking force will kill p units of defender firepower per day, and each unit of defender firepower committed to the battle will kill q units of attacker per day. Also, the kilometer advance on day t can be estimated in terms of the ratio of forces fighting that day as exp c -4a defender firepower attacker firepower b

2 d

Reserves will not be in the battle on day 1, but they may be committed as desired over the ensuing days. Once committed, reserves cannot be withdrawn from the battle. Formulate an NLP model to choose an optimal plan for the defender using the decision variables 1t = 1,

c, 142 xt ! attacker firepower fighting on day t yt ! defender firepower fighting on day t zt ! defender reserve firepower newly committed on day t Assume that forces are lost only to enemy fire.