The Sunco oil company has 2 different processes that can be used to manufacture various types of gasoline. Each process requires mixing different types of oil in the different processes of the company. It costs $5 to run process 1 for one hour and requires 2 barrels of type 1 crude oil and 3 barrels of type 2 crude oil. The result of running process 1 for one hour is 3 barrels of type 1 gasoline and 1 barrel of type 1 gasoline. 2. It costs $6 to run process 2 for one hour and requires 1 barrel of type 1 crude oil and 2 barrels of type 1 gasoline. The result of running process 2 for one hour is 3 barrels of type 3 gasoline. Each week you can buy 300 barrels of type 1 crude for $2 a barrel, and 100 barrels of type 2 crude for $3 a barrel. All the gasoline that is produced can be sold at the following prices per barrel: type 1 gasoline, $7; gasoline 2, $10; gasoline 3, $24. There are 100 hours for all processes per week. In addition, it is desired that at least half of what is produced from this input be sold as gasoline 1. Formulate an LP whose solution maximizes revenue minus costs, using the following variables:

G1 = barrels of type 1 gasoline sold

G2 = barrels of type 2 gasoline sold

G3 = barrels of type 3 gasoline sold

G1P = barrels of type 1 gasoline that are produced

G1P2 = barrels of gasoline type 1 that are sent to process 2

P1 = hours that process 1 runs

P2 = hours that process 2 runs

BC1 = barrels of type 1 crude purchased

BC2 = barrels of type 2 crude purchased

Note. It assumes that the number of barrels of all types must be whole numbers, the hours that the processes run can be fractional.