1. The lines bounding the feasible region for the following linear program are shown on the right below. They are labeled according to which inequality generated them.
   

   Minimize:	3X	+	7Y
   Subject to:	3X	+	2Y	≤	12	(1)
   	X	+	2Y	≥	4	(2)
   	X			≥	1	(3)
   			Y	≤	1	(4)
   	X			≥	0
   			Y	≥	0

   
   a) (15 points) Shade in the feasible region.

   b) (25 points) What is the optimal solution to this problem? Circle the point corresponding to this solution on the graph above.

    

    

    

    

    

   e) (20 points) What is the slack associated with inequality (2)? Show your work.

    

    

2. Interesting Investment Corp. (IIC) is putting together a proposal for a client who's considering investing up to $100,000 with their company. Listed below are the stocks they're considering for inclusion in the account, along with the stocks' projected annual returns, and minimum possible purchase. In addition, the client has asked IIC to construct the portfolio so that no more than $75,000 is invested in any single stock.

   Stock	Projected return (%)	Minimum purchase ($)
   Fabulous Fish	5	20,000
   Genuine Gum	3	5000

   
   IIC has asked you to formulate a linear programming model to help with this decision by answering the questions below.

   a) (5 points) Define (describe and give names to) the decision variables in this problem.

    

    

   b) (10 points) Write the objective function in terms of these decision variables.

    

    

   c) (25 points) Write the constraint inequalities in terms of these decision variables.

Bonus: (5 points) What do you think the optimal solution is in the problem above? Briefly explain your reasoning.