Guanming wants to paint houses and commercial buildings during his summer vacation. He has two types of customers—residential and commercial. The profit from a residential property is HKD500 and from a commercial property, HKD750. A residential property takes 3 hours to paint while a commercial, 4 hours. He likes to work for 48 hours a week. He has a budget of HKD600 per week toward brushes and other consumables. A residential property needs HKD80 toward such tools and consumables, while a commercial property, HKD40. He decides based on his experience that he cannot get more than 6 residential jobs and 8 commercial jobs. He wants to know how many residential and commercial jobs he should complete to maximize his profits.
a. Formulate a linear programming model to this problem.
b. Solve this model graphically.