Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 11% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Bean Brazilian Natural 75% Colombian Mild 25% Blend Regular DeCaf 35% 65% Romans sells the Regular blend for $3.2 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 900 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.89 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.09 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. Let BR-pounds of Brazilian beans purchased to produce Regular BD = pounds of Brazilian beans purchased to produce DeCaf CR= pounds of Colombian beans purchased to produce Regular CD= pounds of Colombian beans purchased to produce DeCaf If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) The complete linear program is Max s.t. BR+ BR BR BD+ BD + CR+ CR |+|| CR BD BR, BD, CR, CD 20 + CD CD CDI=
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 11% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Bean Brazilian Natural 75% Colombian Mild 25% Blend Regular DeCaf 35% 65% Romans sells the Regular blend for $3.2 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 900 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.89 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.09 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. Let BR-pounds of Brazilian beans purchased to produce Regular BD = pounds of Brazilian beans purchased to produce DeCaf CR= pounds of Colombian beans purchased to produce Regular CD= pounds of Colombian beans purchased to produce DeCaf If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) The complete linear program is Max s.t. BR+ BR BR BD+ BD + CR+ CR |+|| CR BD BR, BD, CR, CD 20 + CD CD CDI=
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
1
Transcribed Image Text:Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of
Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 11% higher than the market
price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows:
Blend
Regular DeCaf
Bean
Brazilian Natural 75%
Colombian Mild 25%
Romans sells the Regular blend for $3.2 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 900 pounds of Romans Regular coffee and 500 pounds
of Romans DeCaf coffee. The production cost is $0.89 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.09 per pound. Packaging costs for both products are $0.25 per pound.
Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.
Let BR = pounds of Brazilian beans purchased to produce Regular
BD = pounds of Brazilian beans purchased to produce DeCaf
CR = pounds of Colombian beans purchased to produce Regular
CD = pounds of Colombian beans purchased to produce DeCaf
Max
s.t.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
The complete linear program is
35%
65%
BR+
BR
BR
BD +
BD
CR +
CR
CR
BD
BR, BD, CR, CD ≥ 0
+
+
CD
CD=
=
CD=
Transcribed Image Text:What is the contribution to profit?
Optimal solution:
BR =
BD =
CR =
CD =
If required, round your answer to two decimal places.
Value of the optimal solution = $
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 2 steps with 4 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.