江西財(cái)經(jīng)大學(xué)運(yùn)籌學(xué) 習(xí)題集答案 (3)

1、 1第三章 第三章 Introduction to linear programming 1 下面的表格總結(jié)了兩種產(chǎn)品 A 和 B 的關(guān)鍵信息以及生產(chǎn)所需的資源 Q、R、S： 每單位產(chǎn)品資源使用量 資源 產(chǎn)品 A 產(chǎn)品 B 可用資源 Q R S 2 1 3 1 2 3 2 2 4 利潤/單位 3000 美元 2000 美元 滿足所有線性規(guī)則假設(shè)。 a． 在電子表格上為這一問題建立線性規(guī)劃模型。 b． 用代數(shù)方法建立一個(gè)相

2、同的模型。 c． 用圖表法求解這個(gè)模型。 解： a) 1 2 3 4 5 6 7 8910A B C D E FProduct A Product B Unit Profit $3,000 $2,000 Resource Resource Used Available Resource Q 2 1 2 <= 2 Resource R 1 2 2 <= 2 Resource S 3 3 4 <= 4Product A P

3、roduct B Total Profit Units Produced 0.667 0.667 $3,333.33Resource Usage per Unit Producedb) Let A = units of product A produced B = units of product B produced Maximize P = $3,000A + $2,000B, subject to 2A + B ≤ 2 A +

4、 2B ≤ 2 3A + 3B ≤ 4 and A ≥ 0, B ≥ 0. 3解：a) As in the Wyndor Glass Co. problem, we want to find the optimal levels of two activities that compete for limited resources. Let x1 be the fraction purchased of the partner

5、ship in the first friends venture. Let x2 be the fraction purchased of the partnership in the second friends venture. The following table gives the data for the problem: Resource Usage per Unit of Activity Amount of

6、 Resource 1 2 Resource Available Fraction of partnership in first friends venture 1 0 1 Fraction of partnership in second friends venture 0 1 1 Money $5000 $4000 $6000 Summer Work Hours 400 500 600 Unit Pro

7、fit $4500 $4500 b) The decisions to be made are how much, if any, to participate in each venture. The constraints on the decisions are that you can’t become more than a full partner in either venture, that your money

8、 is limited to $6,000, and time is limited to 600 hours. In addition, negative involvement is not possible. The overall measure of performance for the decisions is the profit to be made c) First venture: (fraction of

9、1st) ≤ 1 Second venture: (fraction of 2nd) ≤ 1 Money: 5000 (fraction of 1st) + 4000 (fraction of 2nd) ≤ 6000 Hours: 400 (fraction of 1st) + 500 (fraction of 2nd) ≤ 600 Nonnegativity:(fraction of 1st) ≥ 0, (fraction of