※ [本文轉錄自 FCU_Talk 看板] 作者: loveadan (冷情魅燕) 看板: FCU_Talk 標題: [考題][作業研究][徐沅錫][95下期中考] 時間: Sat Jul 7 20:16:41 2007 [作業研究][徐沅錫][期中考] 一、A company needs to lease warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. Howeve, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement (in thousands of square feet) and the leasing costs (in hundreds of dollars) for the various leasing periods are as follows: ────┬───────ꈠ ───────┬────────── month │Required space Leasing period│cost per 1000 ────┼─────── (months) │square feet leased($00) 1 │ 30 ───────┼──────────ꈊ 2 │ 20 1 │ 650 3 │ 40 2 │ 1000 4 │ 10 3 │ 1350 5 │ 50 4 │ 1600 ────┴───────ꈠ 5 │ 1900 ───────┴──────────ꈊThe objective is to minimize the total leasing cost for meeting the space requirement. Formulate a linear programming model for this problem. 二、A company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following propert -ies: ──────┬──────────────────── │ꈠ Alloy ├──────────────────── Property │ 1 2 3 4 5 ──────┼────────────────────ꈊ percentage of tin │ 60 25 45 20 50 percentage of zinc│ 10 15 45 50 40 percentage of lead│ 30 60 10 30 10 cost($/pound) │ 22 20 25 24 27 ──────┴──────────────────── The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost. Formulate a liner-programming model for this problem. 三、Thriftem Bank is in the process of devising a loan policy that involves a maximum of $12 million. The following table provides the pertinent data about available types of loans. ──────────────────────────── Type of loan Interest rate Bad debt ratio ──────────────────────────── Personal 0.140 0.10 Car 0.130 0.07 Home 0.120 0.03 Farm 0.125 0.05 Commercial 0.100 0.02 ────────────────────────────ꈊ Bad debts are unrecoverable and produce no interest revenue. Competition with other financial institutions requires the bank to allocate at least 40% of the funds to farm and commercial loans. To assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. The bank also has a stated policy of not allowing the overall ratio of bad debts on all loans to exceed 4%. 四、Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: ──────────────────────────ꈊ Supplier ──────────────────────────ꈊ Component 1ꈠ 2 3 ꈱ1 $12 $13 $14 2 $10 $11 $10 ──────────────────────────ꈊ Each supplier has a limited capacity in terms of the total number of compon -ents it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier│ 1 2 3 ────┼────────── Capacity│ 600 1000 800 If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component2, what purchases do you recommend? What is the total purchase cost for the components? --

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