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 Max Brazilian Natural s.t. Colombian Mild Blend Regular DeCaf 75% 25% 40% 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 900 pounds of Romans Regular coffee and 400 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. 60% (a) Formulate 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 Colombian beans purchased to produce DeCaf.)

Practical Management Science

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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A linear programming computer package is needed.
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.
Max
Bean
Brazilian Natural
s.t.
Colombian Mild
Regular % constraint
DeCaf % constraint
Pounds of Regular
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 900 pounds of Romans Regular coffee and 400 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.
Pounds of DeCaf
(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 c
Colombian beans purchased to produce DeCaf.)
(BR, BD, CR, CD)
(b) What is the optimal solution?
Need Help?
=
Blend
Regular
Read It
75%
25%
□ Show My Work (Optional) ?
DeCaf
40%
60%
TI
(c) What is the contribution to profit (in $)? (Round your answer to two decimal places.)
Watch It
=
=

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INCORRECT FOR

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 2.033BR+2.582BD+1.868CR+2.418CD

INCORRECT

Pounds of Regular

BR+CR≤900

INCORRECT

Pounds of DeCaf

BD+CD≤400

INCORRECT

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