A company can hire full-time workers who work 40 hours per week, part-time workers who work 30 hours a week, and part-time workers who work 20 hours a week. Full-time workers earn $30 per hour and part-time workers earn $25 per hour. The company can't hire more than 100 full-time workers. The company can't hire more than 150 part-time workers who work 30 hours per week. The company can't hire more than 75 part-time works who work 20 hours per week. However, the company needs to hire at least 175 workers in total. How many of each type of worker should be hired to minimized labor costs?

a) Define the decision variables.

b) Write the objective function.

c) Write the constraints in standard form.