Question 1

A university plans to build a new computer lab for its students for data analysis and simulation modeling. It has determined the number of computers needed each month for the next 12 months based on student enrollment, as given in Table 1.

The university is wondering whether to rent the computers or buy new computers. Computers can be rented for a period of one, two, or three months. Table 2 shows the cost of renting.

Table 2: Cost of renting

The university does not have any computers at the start of the year.

Question 1a

Apply linear programming (LP) to formulate the problem to determine the number of computers the university should rent each month and for how long, so that the total cost of renting is minimum.

Question 1b

Solve the LP model in Question 1a by developing a spreadsheet model. How many computers should the university rent each month and for how long? What is the optimal cost of renting?

You can assume that fractional rental is possible. Present your solutions by rounding up or down the number.