A garden store prepares various grades of pine bark for much: nuggets(x1),mini-nuggets(x2),and chips(x3). The process requires pine bark, machine time,labor time,and storage space.The following model has been developed.
Maximize 9x1 + 9x2 + 6x3 (profit)
Subject to
Bark 5x1 + 6x2 + 5x3 <= 600 pounds
Machine 2x1 + 4x2 + 5x3 <= 660 pounds
Labor 2x1 + 4x2 + 3x3 <= 480 pounds
Storage 1x1 + 1x2 +1x3 <= 150 bags
x1,x2,x3 >= 0
a. What is the marginal value of a pound of pine bark? Over what range is this price value appropriate
b. What is the maximum price the store would be justified in paying for additional pine bark?
c. What is the marginal value of labor? Over what range is this value in effect?
d. The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?
e. If the manager can obtain either additional pine bark or additional storage space,whice one should she choose and how much(assuming additional quantities cost the same as usual)?
f. If a change in the chip operation increased the profit on chips from $6 per bag to $7 per bag,would the optimal quantities change? Would the vaule of the objective function change?If so,what would the new value(s) be?
g. If profits on chips increased to $7 per bag and profits on nuggests decreased by $60,wolud the optimail quantities change? Would the value of the objective funciion change? If so,what would the new value(s) be?
h. If the amount of pine bark available decreased by 15 pounds, machine time decreased by 27 minutes, and storage capacity increased by five bags, would this fall in the range of feasibility for multiple changes? If so,what would the value of the objective function be?
庭园商店准备了不同等级的很多松树树皮：掘金（× 1），小鸡块（× 2），以及芯片（× 3）。这一过程需要松树树皮，机时间，劳动时间，和存储space.The以下模式已经研制成功。
最大化9x1 + 9x2 + 6x3（利润）
除
树皮5x1 + 6x2 + 5x3“=600磅 机2x1 + 4x2 + 5x3“=六百裂敬六英镑
劳动2x1 + 4x2 + 3x3“=四百八十零磅
存储1x1 +亚盘一X3的“= 150袋
× 1，x2，X3的“= 0
字母a.什么是1磅的边际价值的松树树皮？超过这个范围是什么价值的适当价格
湾什么是最高价格的商店将在松树树皮额外支付合理？
角什么是劳动的边际价值？超过这个范围是什么有效的价值轿纳呢？
d.经理获得通过更好地安排时间，更多的机器。更多的机器多少时间可有效地利用这一行动？为什么？
大肠杆菌如果
管理者能获得任何闭源没额外的松树树皮或额外的存储空间，这
一个花园商店准备各种等级的松树树皮为:掘金(x1),mini-nuggets(2),薯片(三)。这个过程需要松树树皮、机时间、劳动时间、存储空间下列模型被开发出来。
9x1 + 9x2 + 6x3最乎罩大化利润()。
主题,
5x1 + 6x2 + 5x3树皮< 600磅
2x1 + 4x2 + 5x3机器< 660磅
劳动2x1 + 4x2 + 3 < = 480磅
存储1x1 + 1x2 +拥有< 150个袋子
三、冷却,x1 > = 0
一。什么是边际价值的一磅重的松树树皮?这是在什么范围内价格合适
b。什么是最大的价格是正当的商店在支付额外的松树树皮?
c。什么是边际价值的劳动吗?这是在什么范围值有效吗?
d。经理获得更多的机器,通过更好的安排。多少额外时间机器可以有效地用于这种操作吗?为什么?
e。如果经理隐顷洞能获得额外的松树树皮或是或附加的存储空间,她应该选择之一,粉碎多少额外费用(假定数量相同的像往常一样)?
f。如果一个变化的利润增加晶片运作从6美元每包薯片,每袋,7美元数量变化的最佳?将创造价值的目标函数改变吗如果这样的话,这个新的价值(s)是什么?
g。如果在芯片的利润增加到$ 7 /袋,利润下降了60美元nuggests上的数灶枯量变化,wolud optimail吗?将价值的目标funciion改变吗?如果这样的话,这个新的价值(s)是什么?
h。如果松树树皮可减少了15磅,机器的时间减少了27分钟,存储容量增加了5个袋子,这倒在范围内的可行性,多变化的?如果是这样的话,会对目标函数的值是什么?
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