For each problem listed below:

• Hand in a complete algebra formulation, including clear definitions for all variables.  You may skip any algebraic simplifications that might arise.
• Create an Excel spreadsheet model of the problem and find an optimal solution with Solver.  Hand in the standard printouts.
   

 Q1. (30 points)  You anticipate the following customer demand and unit production costs costs for one of your company's products over the next 6 months:

You can produce up to 1200 units per month.  You can keep the product in inventory, and your maximum end-of-month inventory capacity is 500 units.  For each month, your inventory cost is $5.55 times the month's average inventory (which you approximate as the average of the month's beginning and ending inventory).  It is now the beginning of month 1, and you have 300 units in inventory.  To give yourself some leeway in meeting unknown demands after month 6, you want to end month 6 with at least 200 units in inventory.  Determine how to meet all six month's customer demand at the lowest possible total cost.
 

Q2.  (35 points)  You have recently opened a facility that composts local yard and supermarket waste into fertilizer.  You process four different kinds of waste:

The "cost per ton" in the above table includes the price paid to the supplier (if any), transportation, and processing.  As you compost the waste, you mix it into three different kinds of fertilizer, called "A", "B", and "C":

For example, you can sell at most 100 tons of fertilizer A at $30 per ton.  The following rules apply to the mixing process:

• Fertilizer A must consist of at least 50% leaf mulch and at most 20% supermarket waste
• Fertilizer B must consist of at least 30% supermarket waste, and at most 25% general yard waste
• Fertilizer C must consist of at most 20% leaf mulch, and at most 20% general yard waste.

How should you operate the composting facility to maximize its profit?
 

Q3.  (35 points)  Problem 31 on page 35 of the course pack (Bexter labs).