The time required to load/unload follows an exponential probability dis- tribution with a mean time of 1 hour per truck (or 24 trucks per day in average). Find the followings： a) What is the probability that there are exactly 8 trucks arrived in one day. b) What is the probability that a special truck requires less than 1 hour ※ 引述《XX9 ( 佛曰: ....)》之銘言： : ※ [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($00) : 1 │ 30 ───────┼──────────ꈊ: 2 │ 20 1 │ 650 : 3 │ 40 2 │ 1000 : 4 │ 10 3 │ 1350 : 5 │ 50 4 │ 1600 : ────┴───────ꈠ 5 │ 1900 : ───────┴──────────ꈊ: The objective is to minimize the total leasing cost for meeting the space : requirement. Formulate a linear programming model for this problem. : 二、A company desires to blend a new alloy of 40 percent tin, 35 percent zinc, : and 25 percent lead from several available alloys having the following propert : -ies: : ──────┬──────────────────── : │ꈠ Alloy : ├──────────────────── : Property │ 1 2 3 4 5 : ──────┼────────────────────ꈊ: percentage of tin │ 60 25 45 20 50 : percentage of zinc│ 10 15 45 50 40 : percentage of lead│ 30 60 10 30 10 : cost($/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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