x1 ? x2? x3?

The chief of police has secured additional funding of t8,000,000 for next years budget. The mayor wants to achieve the following: Number of suspects apprehended for major violent crime (such as homicide or armed robbery) must increase by 40%. Property crime (e.g. theft, vandalism) must decrease by 30% Drug related offences should be reduced by 20%. Chief of Police can allocate the additional budget to hire new detectives, increase the number of uniformed patrols and buy new surveillance equipment. Based on previous experience, he estimates additional funds will have the following impact: Each 1,000,000 spent on hiring new detectives will increase number of suspects apprehended for major violent crime by 8% and decrease drug related offences by 2%. Each t1,000,000 spent on uniformed patrols will decrease property crime by 5% and drug related offences by 4%. Each t1,000,000 spent on new surveillance equipment will increase number of suspects apprehended for major violent crime by 4% and reduce property crime by 6%. (Assume that linearity assumption holds, that is effects are not multiplicative. e.g. if 2,000,000 is spent on hiring new detectives, number of suspects apprehended for major violent crime will increase by 16% and drug related offences will decrease by 4%.) The chief of police wants to built a goal programming model where X1, X2, X3 are the amount of additional budget allocated to hiring new detectives, uniformed patrols and surveillance equipment, respectively (in millions of t). Moreover, G is the major violent crime goal, G2 is property crime goal and G3 is drug crime goal. If G3 is most important and G2 is least important, what would be the optimum solution