一个“现实”问题：Product-Mix This corporation has 10 plants in various parts of the world.Each of these plants produces the same 10 products and then sells them within its region.The de- mand (sales potential)for each of these products from each plant is known for each of the next 10 months.Although the amount of a product sold by a plant in a given month cannot exceed the demand,the amount produced can be larger,where the excess amount would be stored in inventory (at some unit cost per month)for sale in a later month 每个厂有10条生产线，可以安排任何产品，但效率和成本可能不 同。必要时也可以考虑在厂间运输成品，特定两个厂之间单位产品运 输成本是固定的。每个厂存储能力有上限，单位成本相同。 Management now needs to determine how much of each product should be produced by each machine in each plant during each month,as well as how much each plant should sell of each product in each month and how much each plant should ship of each prod- uct in each month to each of the other plants.Considering the worldwide price for each product,the objective is to find the feasible plan that maximizes the total profit(total sales revenue minus the sum of the total production costs,inventory costs,and shipping costs)
一个“现实”问题：Product-Mix 每个厂有10条生产线，可以安排任何产品，但效率和成本可能不 同。必要时也可以考虑在厂间运输成品，特定两个厂之间单位产品运 输成本是固定的。每个厂存储能力有上限，单位成本相同
问题4： 你能否估计一下这个问题 66 规模”有多大？ 1000prodvariables:n for each combntion of a pat,machne,produt and month 1,000 inventory variables:one for each combination of a plant,product,and month 1,000 sales variables:ne for each combination of a plant,product,and month shipping variables:n for each ombination of a produt,month,plant (the fromplant),and another plant (the toplant)
线性规划问题的标准形式 n maximize ∑ jxj = subject to i≤b fori=1,2,..,m ≥0forj=1,2,.,n maximize CTx subject to Ax ≤ b ≥ 0
线性规划问题的标准形式
minimize -2x1+3x2 subject to X1 X2 三7 X1- 2x2 ≤ 4 X1 ≥ 0 问题5： 为什么说这不是“标准形式
mizing a linear function subject to linear constraints,into standard form.A linear program might not be in standard form for any of four possible reasons: 1.The objective function might be a minimization rather than a maximization. 2.There might be variables without nonnegativity constraints. 3.There might be equality constraints,which have an equal sign rather than a less-than-or-equal-to sign. 4.There might be inequality constraints,but instead of having a less-than-or- equal-to sign,they have a greater-than-or-equal-to sign