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 |

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