Exxoff Company (Blend Problem)
The Exxoff Company must decide upon the blends to be used for this week's gasoline production so as to maximize its profit for this week. Two gasolines must be blended and their characteristics are listed below:
Gasoline Vapor Pressure Octane Number Selling Price (in $/barrel)
Lo-lead ≤ 7 ≥ 80 $10.00
Premium ≤ 6 ≥ 100 $12.00
The characteristics of the components from which the gasoline can be blended are shown below:
Component Vapor Pressure Octane Number Available This Week (in barrels)
Cat-Cracked Gas 8 83 2,500
Isopentane 20 109 1,200
Straight Gas 4 74 4,000
The vapor pressure and octane number of a blend is simply the weighted average of the corresponding characteristics of its components. There is no problem to sell all the gasolines produced in this week. Components not used can be sold to “independents” for $8.00 per barrel. Formulate this problem in the linear programming problem form.

中文：（调和问题）
Exxoff 公司必须确定用于本周石油生产的混合原料，以使本周的利润达到最大，生产两种石油，它们的特征值如下：
石油 蒸汽压力 辛烷值 售价($/桶)
Lo-lead ≤ 7 ≥ 80 $10.00
Premium ≤ 6 ≥ 100 $12.00
用于生产石油的混合原料的特征值如下所示：
原料 蒸汽压力 辛烷值 本周可用量(桶)
Cat-Cracked Gas 8 83 2,500
Isopentane 20 109 1,200
Straight Gas 4 74 4,000
每种混合原料的蒸汽压力和辛烷值是其特征值的简单加权平均。
生产的汽油一周内可以成功售出，没有用完的原料可以以每桶8美元的价格出售。
请将此问题用线性规划建模。

以下部分我是已完成的


Algebraic Formulation
定义：
Xij=在产品i 中原料j 的用量 (i=L,P j=C,I,S)→XLC XLI XLS XPC XPI XPS
jNU=原料j 没用完的量（CNU INU SNU）

Maximize profit=10(XLC+ XLI +XLS)+12(XPC +XPI +XPS)＋8(CNU+INU+SNU)

Subject to:
XLC + XPC ≤2500
XLI + XPI ≤1200
XLS +XPS≤4000

8XLC+20XLI+4XLS≤21
83XLC+109XLI+74XLS≥240
8XPC+20XPI+4XPS≤18
83XPC+109XPI+74XPS≥300