[Optimization] Codes Answer to online quiz 1

Matlab with cvx: 

% Decision Variables
cvx_begin
    variables xsb xre xc xs
 
    % Objective Function
    maximize(0.04*xsb + 0.06*xre + 0.08*xc + 0.09*xs)
 
    % Constraints
    subject to
        xsb + xre + xc + xs == 2.5e6
        xc + xs <= 2*xsb
        xs <= xc
        xc <= 1.7*xre
        xsb >= 0
        xre >= 0
        xc >= 0
        xs >= 0
cvx_end
 
% Display the optimal solution
fprintf('Optimal Solution:\n');
fprintf('State Bonds: %.1f euros\n', xsb);
fprintf('Real Estate Loans: %.1f euros\n', xre);
fprintf('Car Loans: %.1f euros\n', xc);
fprintf('Scholarship Loans: %.1f euros\n', xs);

Python:

import cvxpy as cp
 
# Decision Variables
xsb = cp.Variable()
xre = cp.Variable()
xcℓ = cp.Variable()
xsℓ = cp.Variable()
 
# Objective Function
objective = cp.Maximize(0.04*xsb + 0.06*xre + 0.08*xcℓ + 0.09*xsℓ)
 
# Constraints
constraints = [
    xsb + xre + xcℓ + xsℓ == 2.5e6,
    xcℓ + xsℓ <= 2*xsb,
    xsℓ <= xcℓ,
    xcℓ <= 1.7*xre,
    xsb >= 0,
    xre >= 0,
    xcℓ >= 0,
    xsℓ >= 0
]
 
# Solve the problem
problem = cp.Problem(objective, constraints)
problem.solve()
 
# Display the optimal solution
print("Optimal Solution:")
print(f"State Bonds: {xsb.value:.1f} euros")
print(f"Real Estate Loans: {xre.value:.1f} euros")
print(f"Car Loans: {xcℓ.value:.1f} euros")
print(f"Scholarship Loans: {xsℓ.value:.1f} euros")