production of 1,100 pounds of Romans Regular coffee and 600 pounds of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. (a) 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, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max = s.t. Regular % constraint=
production of 1,100 pounds of Romans Regular coffee and 600 pounds of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. (a) 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, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max = s.t. Regular % constraint=
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
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 10% 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 | Blend | |
|---|---|---|
| Regular | DeCaf | |
| Brazilian Natural | 75% | 40% |
| Colombian Mild | 25% | 60% |
Romans sells the Regular blend for $3.60 per pound and the DeCaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1,100 pounds of Romans Regular coffee and 600 pounds of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound.
(a)
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, and CD = pounds of Colombian beans purchased to produce DeCaf.)
Max =
s.t.
Regular % constraint=
DeCaf % constraint=
Pounds of Regular=
Pounds of DeCaf=
DeCaf % constraint=
Pounds of Regular=
Pounds of DeCaf=
(b)
What is the optimal solution?
(BR, BD, CR, CD) =
(c)
What is the contribution to profit (in $)? (Round your answer to two decimal places.)
![### Linear Programming Problem for Maximizing Coffee Profit
**Context:**
Romans Food Market, based in Saratoga, New York, offers a variety of specialty foods from around the world. Among its leading products are Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans. The beans are purchased from a distributor in New York City at prices 10% higher than the market price for immediate orders. The current market prices are $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild beans.
#### Coffee Bean Compositions:
| Bean | Blend | Regular | DeCaf |
|-----------------|---------|---------|-------|
| Brazilian Natural | | 75% | 40% |
| Colombian Mild | | 25% | 60% |
Romans sells the Regular blend for $3.60 per pound and the DeCaf blend for $4.40 per pound. The production costs are $0.80 per pound for the Regular blend and $1.05 per pound for the DeCaf blend, with additional packaging costs of $0.25 per pound for both products.
Romans intends to order Brazilian and Colombian coffee beans sufficient to produce 1,100 pounds of Romans Regular coffee and 600 pounds of Romans DeCaf coffee.
#### Problem Statement:
Formulate a linear programming model to determine the optimal amounts of Brazilian Natural and Colombian Mild coffee beans needed to maximize total profit.
**Variables:**
- BR: Pounds of Brazilian beans for Regular coffee
- BD: Pounds of Brazilian beans for DeCaf coffee
- CR: Pounds of Colombian beans for Regular coffee
- CD: Pounds of Colombian beans for DeCaf coffee
Maximize Profit (`Max`):
\[ \text{Total Revenue} - \text{Total Cost} \]
Subject To (s.t.):
1. Regular coffee production:
\[ 0.75 \times BR + 0.25 \times CR = 1100 \]
2. DeCaf coffee production:
\[ 0.40 \times BD + 0.60 \times CD = 600 \]
#### Linear Programming Form:
Max
\[ \text{Total Revenue} - \text{Total Costs} \]
s.t.
\[ 0.75 \times BR + 0.25 \times CR = 1100 \]
\[ 0.40 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3667c4e2-dfba-4518-b7aa-6b434ae74977%2F19c4ad78-6023-4d27-83f1-2efb0e04f6a0%2Fbjdavcm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Programming Problem for Maximizing Coffee Profit
**Context:**
Romans Food Market, based in Saratoga, New York, offers a variety of specialty foods from around the world. Among its leading products are Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans. The beans are purchased from a distributor in New York City at prices 10% higher than the market price for immediate orders. The current market prices are $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild beans.
#### Coffee Bean Compositions:
| Bean | Blend | Regular | DeCaf |
|-----------------|---------|---------|-------|
| Brazilian Natural | | 75% | 40% |
| Colombian Mild | | 25% | 60% |
Romans sells the Regular blend for $3.60 per pound and the DeCaf blend for $4.40 per pound. The production costs are $0.80 per pound for the Regular blend and $1.05 per pound for the DeCaf blend, with additional packaging costs of $0.25 per pound for both products.
Romans intends to order Brazilian and Colombian coffee beans sufficient to produce 1,100 pounds of Romans Regular coffee and 600 pounds of Romans DeCaf coffee.
#### Problem Statement:
Formulate a linear programming model to determine the optimal amounts of Brazilian Natural and Colombian Mild coffee beans needed to maximize total profit.
**Variables:**
- BR: Pounds of Brazilian beans for Regular coffee
- BD: Pounds of Brazilian beans for DeCaf coffee
- CR: Pounds of Colombian beans for Regular coffee
- CD: Pounds of Colombian beans for DeCaf coffee
Maximize Profit (`Max`):
\[ \text{Total Revenue} - \text{Total Cost} \]
Subject To (s.t.):
1. Regular coffee production:
\[ 0.75 \times BR + 0.25 \times CR = 1100 \]
2. DeCaf coffee production:
\[ 0.40 \times BD + 0.60 \times CD = 600 \]
#### Linear Programming Form:
Max
\[ \text{Total Revenue} - \text{Total Costs} \]
s.t.
\[ 0.75 \times BR + 0.25 \times CR = 1100 \]
\[ 0.40 \
Expert Solution
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 5 steps with 4 images
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,
