### Provide the mathematical formulation of the problem

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Felix Navidad, an independent artist, paints large sculptured seasonal - themed figurines for sale during the holiday season. This year he will focus on painting and selling Santa Claus and Reindeer figurines. Each Santa sold will generate a net profit contribution of \$ 27 and each Reindeer will provide a contribution of \$ 33.75 . Each Santa requires 2 hours of painting and each reindeer 2.5 hours. Felix will have 180 hours to devote to painting this season. Felix will purchase the unpainted figurines and has decided, based on past experience, to spend no more than \$ 375 and \$ 540 respectively to purchase the unpainted San tas and reindeers. Each unpainted reindeer costs \$ 12 and each unpainted Santa \$ 10 . Felix has an empty storage barn on his property that has sufficient space to store as many figurines as he may need to purchase.

1. Given the information covered in the course so far, determine the type of problem represented above. What assumptions did you make in coming to this determination?

2. Provide the mathematical formulation of the problem

3. Indicate, based on what we have covered in this course, the various methods that can be used to solve this type of problem.

4. If you think that the graphical method is an appropriate method for solving this problem, use it to solve the problem.

5. What is the optimal solution to the problem (the values of the decision variables) and the objective function value at the optimal solution?

6. Describe the special features, if any, of the solution.

7. Felix has asked you for advice on implementing this solution. What advice would you give him?

8.You have some concerns about the way that Felix has determined how much he is willing to invest in purchasing Santas (\$375) and reindeers (\$540). Suppose his wife has just contributed an additional \$600 towards the purchase of the unpainted figurines, suggest at least one modification to the investment constraints in the model that you developed in part 2 that might provide a higher profit for Felix?

9. Determine whether the modification you suggested in part 8 results in higher profits.

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