An oil company has two refineries. Refinery A produces 200 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000 barrels of low-grade oil. What is the minimum cost to operate both refineries?

$56,000

Step-by-step explanation:

If x is the number of days that Refinery A is in operation, and y is the number of days that Refinery B is in operation, then:

200x + 100y ≥ 800

300x + 100y ≥ 900

200x + 200y ≥ 1000

The total cost is:

C = 12,000x + 10,000y

x and y must be integers.  Possible combinations are:

x = 0, y = 9

x = 1, y = 6

x = 2, y = 4

x = 3, y = 2

x = 4, y = 1

x = 5, y = 0

The costs of these combinations are:

The minimum cost is $56,000.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068