Ted Mosby owns Mosby’s Bikes. Most of Ted’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. A road-racing bike costs $1,200, a cross-country bike costs $1,700, and a mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100, and mountain bikes for $1,200. 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, Ted wants to stock at least twice as many mountain bikes as the other two combined, because mountain bikes sell better.
Formulate and solve the linear programming model for this problem. Ignore the fact that the number of bikes should be integer valued and use the sensitivity report to answer Parts b, c, and d. (Your answer must use and credit the correct part of the sensitivity report. If you formulate and solve the model itself, you will not receive any credit.)
Should Ted try to increase his budget for purchasing bikes, increase space to stock bikes, or increase labor hours to assemble bikes? Why?
If Ted were to hire an additional worker for 30 hours at $10 per hour, how much additional profit would he make, if any?
If Ted were to reduce the price of a cross-country bike to $1,900, would this affect the original solution?