Code not working properly

TICKET_PRICE = 10

tickets_remaining = 100


while tickets_remaining >= 1:

    print("There are {} tickets remaining.".format(tickets_remaining))


    name = input("What is your name? ")


    num_tickets = input("How many tickets would you like, {}? ".format(name))
    num_tickets = int(num_tickets)

    amount_due = num_tickets * TICKET_PRICE

    print("The total due is ${}".format(amount_due))


proceed = input("Would you like to buy these? [Y/N]")
proceed = proceed.lower()
if proceed == 'y':
    print("Sold!")
    tickets_remaining -= num_tickets
else:
    print("Thank you anyways, {}".format(name))

print("Sorry the tickets are all sold out")