Question

South Coast Papers wants to mix two lubricating oils (A and B) to create a mix that has a viscosity rating of no less than 40. A has a viscosity rating of 45 and costs 60 cents per gallon; B has a viscosity rating of 37.5 and costs 40 cents per gallon. There are 2,000 gallons of A and 4,000 gallons of B available.

The company needs no less than 3,000 gallons of the mix to run the machines next month. It has a maximum oil storage capacity of 4,000 gallons. When lubricating oils are mixed, the amount of mix obtained is exactly equal to the sum of the amounts put in. The viscosity rating is the weighted average of the individual viscosities, weighted in proportion to their volumes.

How many gallons of A and how many gallons of B to use in the mix to minimize the total cost, while meeting all the constraints stated above? Formulate the LP model for the problem. (Hint: Suppose X amount of Oil A is mixed with Y amount of Oil B. The viscosity rating of the mix = (45X + 37.5Y)/(X + Y)

Answer 1

Decision variable:

Let,

X = gallons of oil A to create mix

Y = gallons of oil B to create mix

Objective Function:

Objective is to minimize the total cost of blending.

Min. Z = 0.6X + 0.4Y

Subject To:

Gallons of Mixture required	X + Y >= 3000
Oil storing capacity	X + Y <= 4000
Availability of Oil A	X <= 2000
Availability of Oil B	Y <= 4000
Viscosity requirement	(45X + 37.5Y)/(X + Y) >= 40 5X – 2.5Y >= 0
Non-negativity Constraint	X, Y >= 0