Problem:
Constraints and objectives functions
State all the assumptions and show all the work. Define your decision variables clearly. Briefly explain the constraints and objectives functions and define all unit of measure.
During the next three months Airco must meet (on time) 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 labor 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 429 hours of skilled hour available. It costs $100 to hold an air conditioner 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) Mathematically define all decision variables, parameters, constraints, and objective function necessary for formulating the LP model whose solution will tell Airco how it can achieve its objective.
b) Write the LP in standard format.
c) Using the favorite software find the optimal values of the decision variables.