For the linear utility u(x1,x2)=3x1+2x2u(x_1,x_2) = 3x_1 + 2x_2u(x1,x2)=3x1+2x2 with budget 2x1+3x2≤M2x_1 + 3x_2 \leq M2x1+3x2≤M, x1,x2≥0x_1, x_2 \geq 0x1,x2≥0, the Lagrangian is L(x1,x2;λ)=3x1+2x2+λ[M−2x1−3x2].L(x_1,x_2;\lambda) = 3x_1 + 2x_2 + \lambda[M - 2x_1 - 3x_2].L(x1,x2;λ)=3x1+2x2+λ[M−2x1−3x2]. Determine the equilibrium (x1∗,x2∗,λ∗)(x_1^*, x_2^*, \lambda^*)(x1∗,x2∗,λ∗).
(x1∗=M/2, x2∗=0, λ∗=3/2)(x_1^* = M/2,\ x_2^* = 0,\ \lambda^* = 3/2)(x1∗=M/2, x2∗=0, λ∗=3/2)
(x1∗=0, x2∗=M/3, λ∗=2/3)(x_1^* = 0,\ x_2^* = M/3,\ \lambda^* = 2/3)(x1∗=0, x2∗=M/3, λ∗=2/3)
(x1∗=M/2, x2∗=0, λ∗=2/3)(x_1^* = M/2,\ x_2^* = 0,\ \lambda^* = 2/3)(x1∗=M/2, x2∗=0, λ∗=2/3)
(x1∗=0, x2∗=M/3, λ∗=3/2)(x_1^* = 0,\ x_2^* = M/3,\ \lambda^* = 3/2)(x1∗=0, x2∗=M/3, λ∗=3/2)
