Low- Sulphur and High-Sulphur Crude

* it produces low- sulphur and high-sulphur crude from coal and shale.

* order for 10,000 gallons of low-sulphur and 5,000 gallons of high-sulphur crude

* only 100 tons of coal and 150 tons of shale remain unallocated

* Kendra and her team assume that 100 tons of coal and 100 tons of shale are available each quarter for producing the crudes

* coal costs US$20 per ton and the shale US$25 per ton

* low-sulphur crude sells for US$0.50 per gallon and high sulphur crude for US$0.30.

* A gasification batch requires 1 ton of coal and 2 tons of shale to yield 100 gallons of low-sulphur crude and 200 gallons of high-sulphur crude.

* Under pressurisation, each batch requires 2 tons of coal and 1 ton of shale to yield 150 gallons of low-sulphur crude and 100 gallons of high-sulphur crude.

* The initial inventory of both high-sulphur and low-sulphur crude is 0

* Management wants to end the second quarter with 1,000 gallons of each type of crude

* variable labour cost for a gasification batch is $10 and $8 for a pressurization batch.

* Crude not used in a quarter can be used in future periods.

* The annual inventory holdings cost is 8% of the value of the crude.

calculate its corresponding profit.

determine the number of gasification and pressurization batches and the number of gallons of low-sulphur and high-sulphur crude to be produced during each of the next two quarters of the coming year that will minimize costs.

1. Formulate a linear programming model that will help the refinery manger to make a decision about the number of gasification and pressurization batches to schedule and the quantities of low-sulphur crude to produce each quarter. Make sure that the decision variables are well defined. Use a software of your choice and find a solution to the problem formulated.