Consider the following problem:

Max f(x) = f₁(x_1,x₂) + c₂x₂

s.t. 3x₁+a₁₂x₂ 60

2x₁+a₂₂x₂ 60

x₂ 0, x₁ 0

If f₁(x_1,x₂) = 5 x₁ and the KKT conditions for this quadratic programming are:

2x₁ - 3₁ - 2₂ = 2

c₂ + a₁₂₁ + a₂₂₂ = 0

₁S₁ = 0

₂S₂ = 0

3x₁+a₁₂x₂ S₁² 60 = 0

2x₁+a₂₂x₂ S₂² 60 = 0

where x_{1 ,} x_2, S_1, S₂ 0

show that the problem is a convex programming, and solve the quadratic programming by using the modified simplex method.