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 45 hours of available production time. Manufacturing of a door requires 3 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 1 hour in work area #1 and 4 hours in work area #2. Profit is $8.50 per door and $6.50 per window. a. Define decision variables that will tell how many units to build (doors and windows). b. Sketch the flow of inputs and outputs through the two work areas and out to the customer. c. Develop an objective function that will maximize profits. d. Develop production constraints for work areas #1 and #2.