South Coast Papers wants to mix two lubricating oils (A and
B) for its machines in order to minimize cost. It needs no less than 3,000 gallons in order to run its machines during the next month. It has a maximum oil storage capacity of 4,000 gallons. There are 2,000 gallons of Oil A and 4,000 of Oil B available. The mixed fuel must have a viscosity rating of no less than 40.
When mixing fuels, the amount of oil 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. The following is known: Oil A has a viscosity of 45 and costs 60 cents per gallon; Oil B has a viscosity of 37.5 and costs 40 cents per gallon.
State the objective and the constraints of this problem. Plot all constraints and highlight the feasible region. Use your (by now, well-developed) intuition to suggest a feasible (but not necessarily optimal) solution. Be certain to show that your solution meets all constraints.

Question

Patrick Molan · Accepted Answer

Final Answer : The problem formulation appears below. The only unusual constraint is the fifth one. This begins as the viscosity expression: viscosity = (45A + 37.5B) / (A + B) = 40, which becomes 5A = 2.5B. It is not possible to meet the restrictions with only Oil A or only Oil B. Most students will discover that a combination is required. They need to show that their mix has a high enough viscosity by substituting their quantities into the viscosity inequality (as well as showing that their quantities are within the four volume constraints).

Definitions

Learning Objectives

Learning Objectives

Related questions