1.2.2. An oil refinery can buy two types of oil: light crude oil and heavy crude

Question

1.2.2. An oil refinery can buy two types of oil: light crude oil and heavy crude oil. The cost per barrel is $40 and $34, respectively. The following quantities (in barrels) of gasoline, kerosene, and jet fuel can be produced per barrel of each type of crude oil:

The refinery has contracted to deliver 1,200,000 barrels of gasoline, 500,000 barrels of kerosene, and 300,000 barrels of jet fuel. Formulate, as an LP, the problem of determining how much of each type of crude oil to purchase so as to minimize the cost while meeting the appropriate demands. Are the properties of proportionality, additivity, and divisibility satisfied? Explain.

***Please show all steps & explain the reasoning behind the solution to this Linear Optimization problem. TY.
Best Regards,
J.

1.a.a Light crude oil Heay crudeoil Gasoline ersene et ue 0.3 0.45 0.34 O. 18 o.3b

Explanation / Answer

Light -x

heavy - y

Min Z = 40*x+ 34*y

0.45*x +0.34 *y > 1200000

0.18*x + 0.36*y > 500000

0.32*x +0.22*y > 300000

Solving through excel

we type LHS of each constraint in first column

we get

x = 2599206 , y = 89286

2599206 89286 1199999.94 500000.04 851388.84 Z 107003964

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