Optimization Exercises

Optimization Exercises

Linear Programming (LP) Formulation

Product Mix

You make tables and chairs in your small company. Each table has a profit contribution of $ 30.00, and each chair $15.00. A table, however, uses 24 sq. ft. of wood on average, while a chair uses only 16 sq. ft. Also, it takes 2 hour of labor on average per chair, and 5 hours per table. You have 4800 sq. ft. of wood available for the week, and 750 hundred hours of labor. How many of each would you make to maximize profit?

Scheduling

You manage a 24–hour store where workers can come in at the beginning of any 4 hour interval, starting at midnight, and work an 8-hour shift. Based on store activity levels, the numbers of employees needed during the different 4-hour intervals in the day are given below. What is the minimum number of employees you would need on your payroll overall to meet or exceed the requirements?

Time range

12:00 – 4:00 AM

4:00 – 8:00 AM

8:00 – 12:00 Noon

12:00 – 4:00 PM

4:00 – 8:00 PM

8:00 – 12:00 Midnight

# Employees

needed

Transportation

The matrix below gives the costs of transporting material from each of your factories to each of your warehouse locations. The weekly supply and demand for each factory and warehouse respectively is also given. How much material would you ship from each factory to each warehouse to meet the constraints optimally?

Costs in dollars per unit shipped.