A firm produces two goods. Its total cost per day (in dollars) equals
TC = 144 + 18X - 3X1X2,
where X1 is the number of units of the first good produced per day, and X2 is the number of units of the second good produced per day. Because of commitments to customers, the firm must produce a total of 20 units of the two goods per day. If the firm's managers want to minimize its costs (without violating the commitment to its customers), how many units of each good should it produce per day?