Jim Smith, a Senior in Chemistry, Is Planning the Use $\$ 200$

Essay

Jim Smith, a senior in Chemistry, is planning the use of his time in college. The planning horizon is the last 15 weeks before he graduates. For planning purposes, it may be assumed that he has a maximum of 350 hours of time that could be spent. He also has $2,000 left for all discretionary expenses. He wants to exceed the budget as little as possible. He has to prepare for the 3 courses (thesis, biochemistry, and molecular biology) he is currently registered for. He has to apply for graduate school, which involves a decision on how many schools to apply to. He would like to have two kinds of recreation - movies and sports. An hour spent on his thesis, biochemistry, and molecular biology classes will earn 1 point, 1.2, and 0.9 points, respectively. He needs a minimum of 90 points for his thesis, which is a hard constraint. He cannot get more than 100 points in any course. He wants to get as many points as possible, noting that he can not exceed a total of 300 points. Each graduate school application costs $\$ 200$ , takes 20 hours, and has a 0.2 chance of admission. If he applies to 10 schools, his expected number of admissions is $10 *(0.2)=2$ . His goal is to make the expected number of admissions as close to 1.5 as possible without exceeding it. Every movie costs $\$ 20.00$ , gives 5 units of pleasure, and requires 5 hours. Every unit of sports costs $\$ 80$ , gives 12 units of pleasure, and takes 8 hours. He wants to have as close to 60 units of pleasure as possible. The first priority is points for the 3 courses; the second is graduate school; the third is to minimize deviation below the 60 units of pleasure; and the fourth priority is to minimize the pleasure beyond 60 units. Formulate a goal programming model.