Q2. Consider the following situation: A farmer owns a farm which produces watermelon, cucumber, and corn,. There are 12 acres of land available for cultivation. Each crop which is planted has certain requirements for labor and capital. These data along with the net profit figures are given in the following table: Сapital (J.D.) 36 Net profit (J.D.) 40 Labor (hours) 6. Watermelon (per acre) Cucumber (per acre) Corn (per acre) 6. 24 30 2 18 20 The farmer has available 360 JD for capital and knows that there are 48 hours available for working these crops. How much of each crop should be planted to maximize profit? Let x1 : number of acres planted Watermelon, x2: number of acres planted Cucumber, and x3: number of acres planted Corn. We set the mathematical model with the objective function Max. z = 40x1 + 30 x2 + 20 x3. After adding slack variables x4, x5, and x6 ,and solving it by the simplex algorithm, we obtained the following final tableau: X1 X2 X3 X4 X5 X6 X1 1 1 1/4 -1/2 X5 -12 -9/2 1 -9 36 X3 1 -1/4 3/2 10 10 360 (а) of 48 hours to working the crop. How much of each crop should be planted and what is the new profit? Explain. (b) ) Suppose the farmer is able to hire additional workers who can devote to 60 hours instead Suppose the farmer decides to only plant 10 acres instead of 12 acres. How much of each crop should be planted and what is the new profit? Explain.
Q2. Consider the following situation: A farmer owns a farm which produces watermelon, cucumber, and corn,. There are 12 acres of land available for cultivation. Each crop which is planted has certain requirements for labor and capital. These data along with the net profit figures are given in the following table: Сapital (J.D.) 36 Net profit (J.D.) 40 Labor (hours) 6. Watermelon (per acre) Cucumber (per acre) Corn (per acre) 6. 24 30 2 18 20 The farmer has available 360 JD for capital and knows that there are 48 hours available for working these crops. How much of each crop should be planted to maximize profit? Let x1 : number of acres planted Watermelon, x2: number of acres planted Cucumber, and x3: number of acres planted Corn. We set the mathematical model with the objective function Max. z = 40x1 + 30 x2 + 20 x3. After adding slack variables x4, x5, and x6 ,and solving it by the simplex algorithm, we obtained the following final tableau: X1 X2 X3 X4 X5 X6 X1 1 1 1/4 -1/2 X5 -12 -9/2 1 -9 36 X3 1 -1/4 3/2 10 10 360 (а) of 48 hours to working the crop. How much of each crop should be planted and what is the new profit? Explain. (b) ) Suppose the farmer is able to hire additional workers who can devote to 60 hours instead Suppose the farmer decides to only plant 10 acres instead of 12 acres. How much of each crop should be planted and what is the new profit? Explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Topic Video
Question
Transcribed Image Text:Q2. Consider the following situation:
A farmer owns a farm which produces watermelon, cucumber, and corn,. There are 12 acres of land
available for cultivation. Each crop which is planted has certain requirements for labor and capital.
These data along with the net profit figures are given in the following table:
Сapital
(J.D.)
36
Net profit
(J.D.)
Labor
(hours)
6.
Watermelon (per acre)
Cucumber (per acre)
Corn (per acre)
40
24
30
2
18
20
The farmer has available 360 JD for capital and knows that there are 48 hours available for working
these crops. How much of each crop should be planted to maximize profit?
Let x1 : number of acres planted Watermelon, x2: number of acres planted Cucumber, and x3: number
of acres planted Corn.
We set the mathematical model with the objective function Max. z = 40x1+30 x2 + 20 x3. After
ad
slack variables x4, x5, and x6 ,and solving it by the simplex algorithm, we obtained the following
final tableau:
X1
X2
X3
X4
X5
X6
X1
1
1
1/4
-1/2
6.
X5
-12
-9/2
1
-9
36
X3
1
-1/4
3/2
6.
10
10
360
Suppose the farmer is able to hire additional workers who can devote to 60 hours instead
(а)
of 48 hours to working the crop. How much of each crop should be planted and what is the new profit?
Explain.
(b)
crop should be planted and what is the new profit? Explain.
Suppose the farmer decides to only plant 10 acres instead of 12 acres. How much of each
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
