3. Suppose that two mining companies, Australian Minerals Company (AMC) and South African Mines, Inc. (SAMI), control the only sources of a rare mineral used in making certain electronic components. The companies have agreed to form a car- tel to set the (profit-maximizing) price of the mineral. Each company must decide whether to abide by the agreement (i.e., not offer secret price cuts to customers) or not abide (i.e., offer secret price cuts to customers). If both companies abide by the agreement, AMC will earn an annual profit of $30 million and SAMI will earn an annual profit of $20 million from sales of the mineral. If AMC does not abide and SAMI abides by the agreement, then AMC earns $40 million and SAMI earns $5 million. If SAMI does not abide and AMC abides by the agreement, then AMC earns $10 million and SAMI earns $30 million. If both companies do not abide by the agreement, then AMC earns $15 million and SAMI earns $10 million. a. Develop a payoff matrix for this decision-making