A clothing store is on sale to reduce past collections of clothes in stock. Its warehouse has 300 pairs of pants, 300 T-shirts, and XXXX jewelry accessories (use the last four digits of your student ID number, U00##XXXX, to define the XXXX number). Two combos have been advertised to sell the inventory quickly: Combo A, which includes one pair of pants, two T-shirts, and one accessory, and Combo B, which consists of two pairs of pants, one T-shirt, and one accessory. Combo A profits $120, and Combo B provides a profit of $140. The store needs you to formulate an optimization model to help them find the optimal number of Combo A and B units to get the highest profit possible. Please address the following questions and elaborate on your answers:

1.Formulate the optimization model for this problem: define the decision variables, objective function, and constraints;

2. (10 points) Draw the feasible region for this problem on a piece of paper and upload a picture here (use the Add Stuff tool icon to upload the file).

3. (10 points) Report/write the optimal solution (value of decision variables and objective function);

4. (10 points) Classify the constraints in terms of active and non-active

5. (10 points) Report the slack or surplus of all the model constraints

6.(10 points) Which of the three types of merchandise, pants, T-shirts, or accessories contributes the most to achieving greater profits? Why and how much per unit?

7. (10 points) How much should the profit increase if you had twice the number of jewelry accessories? And Why?

8. (15 points) Should the store sell more Combo B units and reduce the number of Combo A units if Combo B would profit at $200? And Why?

9. (15 points) What would be the problem solution if the jewelry accessories constraint were of the type greater than or equal to? And Why?