Q4. Hashtag Café sells three types of desserts: brownies, chocolate puddings and cheesecakes. Each brownie requires one ounce of sugar, three ounces of cream cheese and one ounce of chocolate. Each chocolate pudding requires two ounces of sugar and four ounces of chocolate. One ounce of sugar and 2 ounces of cream cheese are needed to make a cheesecake. The amounts of sugar, cream cheese and chocolate available are 430 ounces, 460 ounces and 420 ounces, respectively. The profit for each brownie, chocolate pudding and cheesecake are RM3, RM2 and RM5, respectively. Let x₁, x2 and x3 be the number of brownies, chocolate puddings and cheesecakes, respectively, the linear programming model and its associated optimal simplex tableau are given as Maximize z = 3x₁ + 2x₂ + 5x3 Subject to Basic X₂ X3 -Z x₁ + 2x₂ + x3 ≤ 430 (sugar) 3x₁ + 2x3 ≤ 460 (cream cheese) x₁ + 4x₂ S 420 (chocolate) X1, X₂, X3 20 x₁ -0.25 1.5 2 -4 X₂ 1 0 0 0 X3 0 1 0 0 0.5 0 -2 -1 Xs -0.25 0.5 1 -2 X₂₁₂₁ 0 0 1 0 Solution 100 230 20 -1350 (a) If the baker purchases additional amounts of 150 ounces of cream cheese and 110 ounces of chocolate, find the new optimum solution by using sensitivity analysis or post-optimal analysis. Comment on your answer. (b) Determine the feasibility range of the availability of cream cheese.
Q4. Hashtag Café sells three types of desserts: brownies, chocolate puddings and cheesecakes. Each brownie requires one ounce of sugar, three ounces of cream cheese and one ounce of chocolate. Each chocolate pudding requires two ounces of sugar and four ounces of chocolate. One ounce of sugar and 2 ounces of cream cheese are needed to make a cheesecake. The amounts of sugar, cream cheese and chocolate available are 430 ounces, 460 ounces and 420 ounces, respectively. The profit for each brownie, chocolate pudding and cheesecake are RM3, RM2 and RM5, respectively. Let x₁, x2 and x3 be the number of brownies, chocolate puddings and cheesecakes, respectively, the linear programming model and its associated optimal simplex tableau are given as Maximize z = 3x₁ + 2x₂ + 5x3 Subject to Basic X₂ X3 -Z x₁ + 2x₂ + x3 ≤ 430 (sugar) 3x₁ + 2x3 ≤ 460 (cream cheese) x₁ + 4x₂ S 420 (chocolate) X1, X₂, X3 20 x₁ -0.25 1.5 2 -4 X₂ 1 0 0 0 X3 0 1 0 0 0.5 0 -2 -1 Xs -0.25 0.5 1 -2 X₂₁₂₁ 0 0 1 0 Solution 100 230 20 -1350 (a) If the baker purchases additional amounts of 150 ounces of cream cheese and 110 ounces of chocolate, find the new optimum solution by using sensitivity analysis or post-optimal analysis. Comment on your answer. (b) Determine the feasibility range of the availability of cream cheese.
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
Question
Please solve part ' b '
![Q4. Hashtag Café sells three types of desserts: brownies, chocolate puddings and cheesecakes. Each
brownie requires one ounce of sugar, three ounces of cream cheese and one ounce of chocolate.
Each chocolate pudding requires two ounces of sugar and four ounces of chocolate. One ounce
of sugar and 2 ounces of cream cheese are needed to make a cheesecake. The amounts of sugar,
cream cheese and chocolate available are 430 ounces, 460 ounces and 420 ounces, respectively.
The profit for each brownie, chocolate pudding and cheesecake are RM3, RM2 and RMS,
respectively. Let x₁, x2 and x3 be the number of brownies, chocolate puddings and cheesecakes,
respectively, the linear programming model and its associated optimal simplex tableau are given
as
Maximize z = 3x₁ + 2x₂ + 5x3
Subject to
Basic
X2
X3
X₂
-Z
x₁ + 2x₂ + x3 5 430 (sugar)
3x₁ + 2x3 ≤ 460 (cream cheese)
x₂ + 4x₂ S 420 (chocolate)
X1, X2, X3 20
X₁
-0.25
1.5
2
-4
X₂
1
0
0
0
X3
0
1
0
0
0.5
0
-2
-1
Xs
-0.25
0.5
1
-2
X₂
0
0
1
0
Solution
100
230
20
-1350
(a) If the baker purchases additional amounts of 150 ounces of cream cheese and 110 ounces of
chocolate, find the new optimum solution by using sensitivity analysis or post-optimal
analysis. Comment on your answer.
(b) Determine the feasibility range of the availability of cream cheese.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34b44b37-e66b-4c48-a846-aeedd1db2b78%2Ff76ae22c-1c81-471c-a3f4-caf932ce3de0%2Fhucpjw_processed.png&w=3840&q=75)
Transcribed Image Text:Q4. Hashtag Café sells three types of desserts: brownies, chocolate puddings and cheesecakes. Each
brownie requires one ounce of sugar, three ounces of cream cheese and one ounce of chocolate.
Each chocolate pudding requires two ounces of sugar and four ounces of chocolate. One ounce
of sugar and 2 ounces of cream cheese are needed to make a cheesecake. The amounts of sugar,
cream cheese and chocolate available are 430 ounces, 460 ounces and 420 ounces, respectively.
The profit for each brownie, chocolate pudding and cheesecake are RM3, RM2 and RMS,
respectively. Let x₁, x2 and x3 be the number of brownies, chocolate puddings and cheesecakes,
respectively, the linear programming model and its associated optimal simplex tableau are given
as
Maximize z = 3x₁ + 2x₂ + 5x3
Subject to
Basic
X2
X3
X₂
-Z
x₁ + 2x₂ + x3 5 430 (sugar)
3x₁ + 2x3 ≤ 460 (cream cheese)
x₂ + 4x₂ S 420 (chocolate)
X1, X2, X3 20
X₁
-0.25
1.5
2
-4
X₂
1
0
0
0
X3
0
1
0
0
0.5
0
-2
-1
Xs
-0.25
0.5
1
-2
X₂
0
0
1
0
Solution
100
230
20
-1350
(a) If the baker purchases additional amounts of 150 ounces of cream cheese and 110 ounces of
chocolate, find the new optimum solution by using sensitivity analysis or post-optimal
analysis. Comment on your answer.
(b) Determine the feasibility range of the availability of cream cheese.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)