John Davis owns Eastcoasters, a bicycle shop in Millersville. Most of John’s bicycle sales are customer orders; however, he also stocks bicycles for walk-in customers. He stocks three types of bicycles—road racing, cross country, and mountain. The cost of a road racing bike is $1200, a cross-country bike costs $1700, and a mountain bike costs $900. He sells road racing bikes for $1800, cross-country bikes for $2100, and mountain bikes for $1200. He has $12,000 available this month to purchase bikes. Each bike must be assembled; a road racing bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a mountain bike requires 16 hours. 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 they sell better. Formulate and solve a linear programming model for this problem.
a. Should John try to increase his budget for purchasing bikes, get more space to stock bikes, or get additional labor hours to assemble bikes? Why?
b. If, in (a), John hired an additional worker for 30 hours at $10/hr, how much additional profit would he make, if any?
c. If John purchased a cheaper cross-country bike for $1200 and sold it for $1900 would it affect the original solution?