Robin's Nest builds birdhouses and mailboxes which they sell at local craft fairs.
(i) They can build at most 20 birdhouses and at most 15 mailboxes per week.
(II) They realize that they must build at least a total of 12 birdhouses and mailboxes to make the business profitable.
(III) Due to material constraints, the number of mailboxes must be no more than three times the number of birdhouses.
If the cost of producing a birdhouse is $15 and the cost of producing a mailbox is $10, how many of each should they produce in order to minimize their costs?

Question

Robin's Nest builds birdhouses and mailboxes which they sell at local craft fairs.
(i) They can build at most 20 birdhouses and at most 15 mailboxes per week.
(II) They realize that they must build at least a total of 12 birdhouses and mailboxes to make the business profitable.
(III) Due to material constraints, the number of mailboxes must be no more than three times the number of birdhouses.
If the cost of producing a birdhouse is $15 and the cost of producing a mailbox is $10, how many of each should they produce in order to minimize their costs?