Finate Mathematics True or False

Question

True or false.        If all the coefficients a1, a2, …, an in the objective function P = a1x1 + a2x2 + … + anxn are nonpositive, then the only solution of the problem is x1 = x2 = … = xn and P = 0.

 

 

Why?

Answer 1

TRUE: Since all variables x₁, x₂, …, xn ≥ 0 (non-negativity constraint) and all coefficients are nonpositive, increasing any variable can only decrease or keep P at 0. Therefore P is maximized at x₁ = x₂ = … = xn = 0, giving P = 0.