Ray Brown owns Ray’s Speed, a bicycle shop. Most of Ray’s bicycle sales are customer order; however, he also stocks bicycle for walk-in customer. He stocks three types of bicycles; road- racing, cross-country, and mountain. A road-racing bike cost $1200, a cross-country bike costs $1700, and a mountain bike costs $900. He sells road-racing bikes for $1800, 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, he wants to stock at least twice as many mountain bikes as the other two combined because mountain bikes sell better.
a. solve this problem
b. should Ray try to increase his budget for purchasing bikes, increase space to stock bikes, or increase labor hours to ensemble bikes? why?
c. if ray hired an additional worker for 30 hours at $10 per hour, how much additional profit would he make, if any?
d. if ray purchased a cheaper cross-country bike for $1,200 and sold it for $1,900, would this affect the original solution?
This is the instruction for the problem:
It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.
Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.
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