pro9. Tree Nursery Mario Cekada owns a tree nursery businesMario can sell a weeping Japanese maple of a certain size fo$350 in profit. He can sell tricolor beech trees of a certain size for$500 profit. The travel time to acquire the Japanese maple trees s5 hours while the travel time for the beech trees is 7 hours Thedigging process takes 1 hour for the Japanese maple trees and2hours for the becch trees. Both kinds of trees require 4 hours oftime to deliver to the client. In a particular season, Mario hasavailable 3600 work hours for travel time to acquire the trees, 900work-hours for digging, and 2600 work-hours for delivery to theclients. How many trees of cach kind should he acquire to makea maximum profit? What is the maximum profit?

Question
Asked Oct 28, 2019
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Use simplex method to solve the problem.

pro
9. Tree Nursery Mario Cekada owns a tree nursery busines
Mario can sell a weeping Japanese maple of a certain size fo
$350 in profit. He can sell tricolor beech trees of a certain size for
$500 profit. The travel time to acquire the Japanese maple trees s
5 hours while the travel time for the beech trees is 7 hours The
digging process takes 1 hour for the Japanese maple trees and2
hours for the becch trees. Both kinds of trees require 4 hours of
time to deliver to the client. In a particular season, Mario has
available 3600 work hours for travel time to acquire the trees, 900
work-hours for digging, and 2600 work-hours for delivery to the
clients. How many trees of cach kind should he acquire to make
a maximum profit? What is the maximum profit?
help_outline

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pro 9. Tree Nursery Mario Cekada owns a tree nursery busines Mario can sell a weeping Japanese maple of a certain size fo $350 in profit. He can sell tricolor beech trees of a certain size for $500 profit. The travel time to acquire the Japanese maple trees s 5 hours while the travel time for the beech trees is 7 hours The digging process takes 1 hour for the Japanese maple trees and2 hours for the becch trees. Both kinds of trees require 4 hours of time to deliver to the client. In a particular season, Mario has available 3600 work hours for travel time to acquire the trees, 900 work-hours for digging, and 2600 work-hours for delivery to the clients. How many trees of cach kind should he acquire to make a maximum profit? What is the maximum profit?

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Expert Answer

Step 1

Let x be the number of trees acquired of Japanese maple

And y be the number of trees acquired of tricolor beech trees

So, according to the given question the required set of problem is:

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maximize Z 350x+ 500y subject to 5x7y 3600 x +2y900 4x 4y 2600=x+ys650

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Step 2

Now, by adding the slack variables the problem becomes:

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maximize Z 350x 500y0s +Os2 +0s3 subject to 5x 7y s3600 x +2y 900 4x4y2600 x+ y + s =650

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Step 3

Now convert the problem in...

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b S12S3 y 3600 100 =514.28 7 5 3600 S1 (2) 00 00 900 = 450> 2 900 S2 650 = 650 1 1 1 1 650 S3 00 0 z-350-500 1 0

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