A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders?
A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders?
I need to use the Five Step Method for mathematical modeling.
- Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency.
- Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math.
- Formulate the model. Restate the question posed in step 1 in terms of the modeling approach selected in step 2. Here you will be formulating a function in one variable (time) to be optimized.
- Solved the model. Apply the solution procedure for modeling approach selected. Be careful with math involved to avoid errors. Does your solution make sense?
- Answer the question. Rephrase the results of step 4 in nontechnical terms- Plain language with no math jargon or symbols.
SENSITIVITY ANALYSIS: (This is the part I am a bit uncertain about)
1. Preform a sensitivity analysis of the optimal time to sell versus the variable cost to raise a unicorn (harness still $100).
2. So if the actual variable cost was $4.00 per day instead of $5.00 (20% decrease), what would you estimate for the best time to sell based on your sensitivity results?
3. Finally, substitute $4.00 for the variable cost into your previous profit function and find the optimal time to sell.
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