Oil Blending . An oil company produces 3 brands of oil regular multigrade and supreme each brand of oil is composed of one or more of 4 crude stocks each having a different viscocity index the relevent data concering the crude stocks are
|
Crude
Stock
|
Viscocity
Index
|
Cost
($/barrel)
|
Supply per day (barrels)
|
|
1
|
20
|
$ 7.10
|
1000
|
|
2
|
40
|
$ 8.50
|
1100
|
|
3
|
30
|
$ 7.70
|
1200
|
|
4
|
55
|
$ 9.00
|
1100
|
each brand of oil must meet a min standard for viscocity index and each brand thus sell the different price . The relevant data concerning the three brands of oil are
|
Brand
|
Minimum
Viscocity
Index
|
Selling price
($/barrel)
|
Daily demand
(Barrels)
|
|
Regular
|
25
|
$ 8.50
|
2000
|
|
Multi Grade
|
35
|
$ 9.00
|
1500
|
|
Supreme
|
50
|
$10.00
|
750
|
Determine an optimal production plan for a single day assuming that all oil produced during this day can be either stored or sold at negiliable cost. What is the optimal mix to meet customer demand and maximize profit?