Greasy Oil (GO) processes crude oil to produce three products, A, B and C. Crude oil costs $70 per barrel landed at the refinery and $40 per barrel to refine.
After some volume losses in the refinery, the yield from each barrel of crude oil is 60 litres of Product A, 70 litres of Product B and 20 litres of Product C. Each product requires additional processing before it can be sold. The following table provides the revenue and additional processing cost per litre for each product and the maximum amount of product that can be sold:
Revenue
A
B
C
Additional processing cost
$2.00
$1.50
$0.80
Maximum sales (litres)
0.5
0.2
0.2
16,000
18,000
6,000
Any product produced but cannot be sold is burned to generate steam and saves GO the $.20 per litre it would otherwise pay for fuel to generate the steam.
Given this information, and assuming GO wants to maximize its short-term profit, write the equations for the linear program to solve for the amount of crude oil GO should purchase and refine.
