SOLVE THE LPP - SIMPLEX METHOD    Max.:  P= 30x1 + 70x2   S.t.:  x1 + 2x2 ≤ 20          x1  +5x2 ≤ 35          x1 and x2  ≥ 0

Consider the following nonlinear program. max x(y – 2) s.t. x = 33 - 3y y 2 2 (a) (b) Derive the KKT necessary conditions for the nonlinear Solve the nonlinear program using the KKT necessary conditions. program.

solve to step wise

do fast

i need i) and ii)both do fast

Use the following theorem. = If F(s) L{f(t)} and n = 1,2,3, dots, n n then L{i" f(1)} = (- 1)" d² _F(s). ds n Evaluate the given Laplace transform. (Write your answer as a function of s .) L{4t cos(t)}

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The city has been broken down into 20 geographic areas, each containing 5,000 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 1,000 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) The 1,000…