The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than per- mitting the olives to grow on their own and results in a smaller size olive. It also permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the nor- mal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Be- cause of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the maximum possible profit. (b) the best combination of barrels of pruned and regular olives. (c) the number of acres that the olive grower should devote to each growing process.

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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The seasonal yield of olives in a Piraeus, Greece,
vineyard is greatly influenced by a process of
branch pruning. If olive trees are pruned every two
weeks, output is increased. The pruning process,
however, requires considerably more labor than per-
mitting the olives to grow on their own and results in
a smaller size olive. It also permits olive trees to be
spaced closer together. The yield of 1 barrel of olives
by pruning requires 5 hours of labor and 1 acre of
land. The production of a barrel of olives by the nor-
mal process requires only 2 labor hours but takes 2
acres of land. An olive grower has 250 hours of labor
available and a total of 150 acres for growing. Be-
cause of the olive size difference, a barrel of olives
produced on pruned trees sells for $20, whereas a
barrel of regular olives has a market price of $30.
The grower has determined that because of uncertain
demand, no more than 40 barrels of pruned olives
should be produced. Use graphical LP to find
(a) the maximum possible profit.
(b) the best combination of barrels of pruned and
regular olives.
(c) the number of acres that the olive grower should
devote to each growing process.
Transcribed Image Text:The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than per- mitting the olives to grow on their own and results in a smaller size olive. It also permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. The production of a barrel of olives by the nor- mal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Be- cause of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced. Use graphical LP to find (a) the maximum possible profit. (b) the best combination of barrels of pruned and regular olives. (c) the number of acres that the olive grower should devote to each growing process.
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