(6 points) Goal Programming

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 x_i = 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 i is, for district 1, 40 - 3x₁, and for district 2, 50 - 4x₂. Gotham City has three goals:

Goal 1 Average response time in district 1 should be at most 5 minutes.

Goal 2 Average response time in district 2 should be at most 5 minutes.

Goal 3 At most $100,000 per year should be spent on ambulance service.

Gotham City feels (for each district) that each minute by which average response time fails to meet the 5-minute goal is equivalent to a cost of $10,000, and each dollar by which the budget constraint is exceeded incurs a cost of $1.

Set up and solve an LP model that can be used to determine how many ambulances should be assigned to each district.

Use goal programming model to solve problem, on excel