You have been put in charge of the Melrose oil refinery. The refinery produces gas and hea...

You have been put in charge of the Melrose oil refinery. The refinery produces gas and heating oil from crude oil. Gas sells for $8 per barrel and must have an average “grade level” of at least 9. Healing oil sells for $6 a barrel and must have an average grade level of at least 7. At most, 2,000 barrels of gas and 600 barrels of heating oil can be sold. Incoming crude can be processed by one of three methods. The per barrel yield and per barrel cost of each processing method are shown in Table 32. For example, if we refine 1 barrel of incoming crude by method 1, it costs us $3.40 and yields .2 barrels of grade 6, .2 barrels of grade 8, and .6 barrels of grade 10.

Before being processed into gas and heating oil, processed grades 6 and 8 may be sent through the catalytic cracker to improve their quality. For $1.30 per barrel, a barrel of grade 6 may be “cracked” into a barrel of grade 8. For $2 per barrel, a barrel of grade 8 may be cracked into a barrel of grade 10. Any leftover processed or cracked oil that cannot be used for heating oil or gas must be disposed of at a cost of $0.20 per barrel. Determine how to maximize the refinery’s profit.

table 32