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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