A poker company assembles three different poker sets. Each Royal Flush poker set contains 1000 poker chips, 10 decks of cards, 4 dice, and 2 dealer buttons. Each Deluxe Diamond poker set contains 600 poker chips, 5 decks of cards, 2 dice, and one dealer button. The full House porker set contains 300 poker chips, 5 decks of cards, 2 dice, and one dealer button. The company has 2,900,000 poker chips, 25,000 decks of cards, 10,000 dice, and 6500 dealer buttons in stock. They earn a profit of $38 for each Royal Flush poker set, $22 for each Deluxe Diamond poker set, and $12 for each Full House poker set.
1. How many of each type of poker set should they assemble to maximize profit? What is the maximum profit?
2. Find the values of any nonzero slack variables and describe what they tell you about any unused components.