Amelia wants to do a part time job during her spring break. She has two jobs now—one in an admissions office and the other in a nearby restaurant. She does not want to work for more than 40 hours per week. She believes that working in the restaurant is easier than working in the admissions office. Since the job at the admissions office demands a high degree of attention, she wants to work more in the restaurant. For every 1 hour of working at the admissions office, she plans to work 2 hours in the restaurant. She wants to work up to 22 hours in the restaurant. She will get a revenue of £9 per hour of work at the admissions office and £7 per hour in the restaurant. She wants to determine the number of hours she should work in the admissions office (x1) and the restaurant (x2) to maximize her earning per week during the spring break.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.