## Why did the oil refinery break up with its significant other? Because they had too many crude differences!

Now let's get to the problem at hand. We need to formulate an LP to determine the optimal purchasing and operating decisions for the refinery. Here's how we can do it:

Let:

- VL = Number of units of Venezuelan crude oil to purchase

- SL = Number of units of Saudi crude oil to purchase

- VS = Number of units of Venezuelan crude oil to process using the Short process

- RS = Number of units of Saudi crude oil to process using the Short process

- VR = Number of units of Venezuelan crude oil to process using the Regular process

- RR = Number of units of Saudi crude oil to process using the Regular process

We need to maximize the total profit, which is the sum of the profits from the Light and Heavy products. The profit from each product is the market value minus the cost. The objective function is:

Maximize: 27(VS + RS + VR + RR) + 25((0.45VS + 0.52RS + 0.49VR + 0.50RR) + (0.60VS + 0.36RS + 0.68VR + 0.32RR))

Subject to the following constraints:

1. The total amount of Venezuelan crude oil processed cannot exceed the available amount: VS + VR <= VL

2. The total amount of Saudi crude oil processed cannot exceed the available amount: RS + RR <= SL

3. The total amount of crude oil processed cannot exceed the refinery's capacity:

VS + RS + VR + RR <= 10,000 (for regular process)

VS + RS + VR + RR <= 13,000 (for short process)

There are also non-negativity constraints for all decision variables:

VS, RS, VR, RR >= 0

Solve this LP, and you'll find the optimal values for the purchasing and operating decisions. Good luck, and may your profits flow like oil!