During the next three months Airco must meet (on lime) the following demands for air conditioners: month 1, 300; month 2,400; month 3, 500. Air conditioners can be produced in either New York or Los Angeles. It takes 1.5 hours of skilled labour to produce an air conditioner in Los Angeles, and 2 hours in New York. It costs $400 to produce an air conditioner in Los Angeles, and $350 in New York. During each month, each city has 420 hours of skilled labour available. It costs $100 to hold an air conditioner in inventory for a month. At the beginning of month 1, Airco has 200 air conditioners in stock. Airco wants to know how to minimize the cost of meeting air conditioner demands for the next three months.

a) Write the LP model for this problem (mathematically define all decision variables, parameters, constrains, and objective function necessary for formulating the LP model whose solution will tell Airco how it can achieve its objective).

b) Using your favourite software find the optimal values and solutions.