Gotham City must determine how to allocate ambulances during the next year. It costs $5000 per year to run an ambulance. Each ambulance must be assigned to one of two districts. Let xi be the number...

Gotham City must determine how to allocate ambulances during the next year. It costs $5000 per year to run an ambulance. Each ambulance must be assigned to one of two districts. Let xi be the number of ambulances assigned to district i, i = 1, 2. The average time (in minutes) it takes for an ambulance to respond to a call from district 1 is 40 - 3x1; for district 2, the time is 50 - 4x2. Gotham City has three goals (listed in order of priority):

■ Goal 1: At most $100,000 per year should be spent on ambulance service.

■ Goal 2: Average response time in district 1 should be at most five minutes.

■ Goal 3: Average response time in district 2 should be at most five minutes.

a. Use goal programming to determine how many ambulances to assign to each district.

b. How does your answer change if goal 2 has the highest priority, then goal 3, and then goal 1?