John Hoke owns Hoke's Spokes, a bike shop. Most of his bicycle sales are customer orders but he also stocks bikes for walk-in customers. He stocks 3 types of bikes: road, cross-country, and mountain. A road bike costs $1200, cross-country $1700, and a mountain bike costs $900. He then sells road bikes for $1800, cross-country for $2100 and mountain bikes for $1200. He has $12,000 available this month to purchase bikes. Each bike must be assembled which takes 8 hours for road bikes, 12 hours for cross-country, and 16 hours for mountain bikes. He estimates that he and his employees have 120 hours available to assemble bikes. He has enough space in his store to order 20 bikes this month. Based on past sales, John wants to stock at least twice as many mountain bikes as the other two combined because mountain bikes sell that much better. Required:
Formulate a linear programming model for this problem.