Question

You are employed to advise a petroleum company on the following problem: The company has three oil plants A, B and C. They want to know how many barrels of crude oil each plant should produce to meet the market demand. Each plant can produce barrels of crude oil, and then convert the crude into motor oil, diesel oil, and gasoline. The capabilities of each of the plants are as follows:

Plant A: From each barrel of crude oil, plant A can produce 25 gallons of motor oil, 15 gallons of diesel, and 5 gallons of gasoline.

Plant B: From each barrel of crude oil, plant B can produce 3 gallons of motor oil, 14 gallons of diesel, and 5 gallons of gasoline.

Plant C: From each barrel of crude oil, plant C can produce 4 gallons of motor oil, 5 gallons of diesel, and 12 gallons of gasoline. The current demand in the local market is for 2280 gallons of motor oil, 1800 gallons of diesel, and 990 gallons of gasoline.

a) Set up linear equations to model this problem, in terms of how many barrels each plant should produce to meet the demand.

b) If plants B and C break down temporarily, how many barrels should plant A produce to meet a demand of 400 gallons of motor oil, 200 gallons of diesel and 100 gallons of gasoline.

c) If plant A breaks down only, and plants B and C are functioning, find an example of quantities of demand for motor oil, diesel, and gasoline which could NOT be met exactly (i.e. without wastage).

Answer 1