An oil company operates two refineries in a certain city. Refinery I has an output of 200, 100, and 100 barrels of low-, medium-, and high-grade oil per day, respectively. Refinery II has an output of 100, 200, and 600 barrels of low-, medium-, and high-grade oil per day, respectively. The company wishes to produce at least 1,000, 1,400, and 3,000 barrels of low-, medium-, and high-grade oil to fill an order. If it costs $500/day to operate refinery I and $700/day to operate refinery II, determine how many days each refinery should be operated to meet the requirements of the order at minimum cost to the company. What is the minimum cost?
A) refinery I for 0 days; refinery II for 10 days; $5,300
B) refinery I for 6 days; refinery II for 4 days; $5,400
C) refinery I for 2 days; refinery II for 6 days; $5,200
D) refinery I for 3 days; refinery II for 5 days; $5,200

Question

Quizplus · Accepted Answer

To meet the minimum requirements for each grade of oil at the lowest cost, we need to find a combination of days that each refinery operates to produce at least 1,000 barrels of low-grade, 1,400 barrels of medium-grade, and 3,000 barrels of high-grade oil. Operating refinery I for 2 days and refinery II for 6 days yields exactly 1,000 barrels of low-grade (200*2 + 100*6), 1,400 barrels of medium-grade (100*2 + 200*6), and 3,200 barrels of high-grade oil (100*2 + 600*6), meeting the order requirements. The cost is $500*2 + $700*6 = $5,200, which is the minimum cost among the options provided.

An Oil Company Operates Two Refineries in a Certain City