PROBLEM 1: LINEAR PROGRAMMING MODEL DEVELOPMENT (40 possible
points) A manufacturer makes two products, doors and windows. Each
must be processed through two work areas. Work area #1 has 60 hours
of available production time. Work area #2 has 48 hours of
available production time. Manufacturing of a door requires 4 hours
in work area #1 and 2 hours in work area #2. Manufacturing of a
window requires 2 hours in work area #1 and 4 hours in work area
#2. Profit is $8 per door and $6 per window. As you respond to the
following questions, please note that you are only setting the
problem up. A solution to determine the number of doors and windows
to be manufactured and the resulting profit is NOT necessary.

1. Define the decision variables that will tell how many units
to build (doors and windows).

2. Develop an objective function that will maximize profits.

3. Develop production constraints for work areas #1 and #2.