Question: Explicitly state the following:

1. Decision Variables: Express the decision variable in mathematical notation, and state what each decision variable stands for in words.
2. Constraints: Write each constraint in mathematical notation, and state what it stands for in words.
3. Objective function: Write the objective in mathematical notation, and state what it stands for in words.
4. Following steps (1) – (3), write the entire model as a linear programming (LP) formulation.
5. Solve the LP using GAMS, and determine the optimal values of: decision variables, objective function, and constraints.

A trucking company with $2,000,000 to spend on new equipment is contemplating purchasing three types of vehicles: A, B, and C. Vehicle A has a 10-ton payload and is expected to cover 55 mi/hr, and costs $40,000. Vehicle B has a 20-ton payload and is expected to cover 50 mi/hr, and costs $65000. Vehicle C is a modified form of B; it carries sleeping quarters for one driver, and this reduces its capacity to 18-tons and raises the cost to $75000.

Vehicle A requires a crew of one man, and if driven on three shifts per day, could be run for an average of 18 hours/day. Vehicles B and C require a crew of two men each, but whereas B can be driven 18 hours/day with three shifts, C can be run an average of 21 hours/day. The company has 150 drivers available each day and would find it difficult to obtain further crews. Maintenance facilities are such that the total number of vehicles must not exceed 30.

How many vehicles of each type should be purchased if the company wishes to maximize its capacity in ton-mi per day?

Price: $2.99

Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document