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Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods

from around the world. Two of the stores 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:

.:.
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 1000 pounds of Romans Regular coffee and 500
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.
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.
What is the optimal solution and what is the contribution to profit?
SOLUTION:
Let

BR

BD

CR

CD

Type of Bean
Brazilian
Colombian

Cost per pound (\$)

1.10(0.47) = 0.517
1.10(0.62) = 0.682

Total revenue = 3.60(BR + CR) + 4.40(BD + CD)

Total cost of beans = 0.517(BR + BD) + 0.682(CR + CD)
Total production cost = 0.80(BR + CR) + 1.05(BD + CD)
Total packaging cost = 0.25(BR + CR) + 0.25(BD + CD)
Total contribution to profit = (total revenue) - (total cost of beans) - (total production
cost)
Total

contribution to profit = 2.033BR + 2.583BD + 1.868CR + 2.418CD

Regular % constraint
BR = 0.75(BR + CR)
0.25BR - 0.75CR = 0
DeCaf % constraint
BD = 0.40(BD + CD)
0.60BD - 0.40CD = 0
Pounds of Regular: BR + CR = 1000
Pounds of DeCaf: BD + CD = 500
The complete linear program is
Max

+ 2.418CD

s.t.
0.25BR

0.60BD

BR

=
0
0.40CD =
0
CR
= 1000
+
CD = 500
BR, BD, CR, CD 0
-

+
BD

0.75CR

250, and

CD = 300.
The text passage describes a business scenario involving the production of two types of coffee blends, Regular and DeCaf, and formulates a linear programming model to maximize profit. It includes a detailed breakdown of costs, revenue, and constraints, and provides an optimal solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Вы находитесь на странице: 1из 3

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods

from around the world. Two of the stores 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:

.:.
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 1000 pounds of Romans Regular coffee and 500
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.
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.
What is the optimal solution and what is the contribution to profit?
SOLUTION:
Let

BR

BD

CR

CD

Type of Bean
Brazilian
Colombian

Cost per pound (\$)

1.10(0.47) = 0.517
1.10(0.62) = 0.682

Total revenue = 3.60(BR + CR) + 4.40(BD + CD)

Total cost of beans = 0.517(BR + BD) + 0.682(CR + CD)
Total production cost = 0.80(BR + CR) + 1.05(BD + CD)
Total packaging cost = 0.25(BR + CR) + 0.25(BD + CD)
Total contribution to profit = (total revenue) - (total cost of beans) - (total production
cost)
Total

contribution to profit = 2.033BR + 2.583BD + 1.868CR + 2.418CD

Regular % constraint
BR = 0.75(BR + CR)
0.25BR - 0.75CR = 0
DeCaf % constraint
BD = 0.40(BD + CD)
0.60BD - 0.40CD = 0
Pounds of Regular: BR + CR = 1000
Pounds of DeCaf: BD + CD = 500
The complete linear program is
Max

+ 2.418CD

s.t.
0.25BR

0.60BD

BR

=
0
0.40CD =
0
CR
= 1000
+
CD = 500
BR, BD, CR, CD 0
-

+
BD

0.75CR

250, and

CD = 300.
user
The text passage describes a business scenario involving the production of two types of coffee blends, Regular and DeCaf, and formulates a linear programming model to maximize profit. It includes a detailed breakdown of costs, revenue, and constraints, and provides an optimal solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER