Lisa, Pam and Martine are in partnership together. Their business manufactures and sells sporting trophies. Lisa, Pam and Martine have agreed to divide the responsibilities of managing the business equally.

Lisa has entered into a contract with a supplier for the purchase of goods on behalf of the partnership. However, Pam and Martine are not aware of this agreement and have not authorised Lisa to make this purchase. When the goods arrive, Pam and Martine refuse to pay for them, claiming that Lisa did not have the authority to enter into the contract on behalf of the partnership.

Explain the legal principles of mutual agency, actual authority and apparent authority using the facts from the above case, and advice Lisa, Pam and Martine about their rights and obligations in relation to the contract with the supplier under these legal principles.