Brendan Quinlan and Maeve Lynch are a couple. They decided to open an Irish restaurant in Changchun, a small town in Northeast China. There were no other Irish restaurants in Changchun, and the possibility of doing something new and somewhat risky intrigued the young people. They purchased an old bistro just off Main Street for their new restaurant, which they named “The Bridge 1988". Brendan and Maeve knew in advance that at least initially they could not offer a full, varied menu of dishes. They had no idea what their local customers' tastes in Irish cuisine would be, so they decided to serve only two full-course meals each night, one with beef and the other with fish. Brendan, their chef, was confident he could make each dish so exciting and unique that two meals would be sufficient, at least until they could assess which menu items were most popular. Brendan indicated that with each meal he could experiment with different appetizers, soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of menu items. The next problem for Brendan and Maeve was to determine how many meals to prepare for each night so they could shop for ingredients and set up the work schedule. They could not afford too much waste. They estimated that they would sell a maximum of 60 meals each night. Each fish meal, including all accompaniments, requires 15 minutes to prepare, and each beef meal takes twice as long. There is a total of 20 hours of kitchen staff labour available each day. Brendan and Maeve believe that because of the health consciousness of their potential clientele they will sell at least three fish meals for every two beef meals. However, they also believe that at least 10% of their customers will order beef meals. The profit from each fish meal will be approximately €12, and the profit from a beef meal will be about €16. a) Formulate a linear programming model for Brendan and Maeve that will help them estimate the number of meals they should prepare each night to maximise the total profit.
Brendan Quinlan and Maeve Lynch are a couple. They decided to open an Irish restaurant in Changchun, a small town in Northeast China. There were no other Irish restaurants in Changchun, and the possibility of doing something new and somewhat risky intrigued the young people. They purchased an old bistro just off Main Street for their new restaurant, which they named “The Bridge 1988". Brendan and Maeve knew in advance that at least initially they could not offer a full, varied menu of dishes. They had no idea what their local customers' tastes in Irish cuisine would be, so they decided to serve only two full-course meals each night, one with beef and the other with fish. Brendan, their chef, was confident he could make each dish so exciting and unique that two meals would be sufficient, at least until they could assess which menu items were most popular. Brendan indicated that with each meal he could experiment with different appetizers, soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of menu items. The next problem for Brendan and Maeve was to determine how many meals to prepare for each night so they could shop for ingredients and set up the work schedule. They could not afford too much waste. They estimated that they would sell a maximum of 60 meals each night. Each fish meal, including all accompaniments, requires 15 minutes to prepare, and each beef meal takes twice as long. There is a total of 20 hours of kitchen staff labour available each day. Brendan and Maeve believe that because of the health consciousness of their potential clientele they will sell at least three fish meals for every two beef meals. However, they also believe that at least 10% of their customers will order beef meals. The profit from each fish meal will be approximately €12, and the profit from a beef meal will be about €16. a) Formulate a linear programming model for Brendan and Maeve that will help them estimate the number of meals they should prepare each night to maximise the total profit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Brendan Quinlan and Maeve Lynch are a couple. They decided to open an Irish restaurant in
Changchun, a small town in Northeast China. There were no other Irish restaurants in
Changchun, and the possibility of doing something new and somewhat risky intrigued the
young people. They purchased an old bistro just off Main Street for their new restaurant, which
they named "The Bridge 1988".
Brendan and Maeve knew in advance that at least initially they could not offer a full, varied
menu of dishes. They had no idea what their local customers' tastes in Irish cuisine would be,
so they decided to serve only two full-course meals each night, one with beef and the other with
fish. Brendan, their chef, was confident he could make each dish so exciting and unique that
two meals would be sufficient, at least until they could assess which menu items were most
popular. Brendan indicated that with each meal he could experiment with different appetizers,
soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of
menu items. The next problem for Brendan and Maeve was to determine how many meals to
prepare for each night so they could shop for ingredients and set up the work schedule.
They could not afford too much waste. They estimated that they would sell a maximum of 60
meals each night. Each fish meal, including all accompaniments, requires 15 minutes to
prepare, and each beef meal takes twice as long. There is a total of 20 hours of kitchen staff
labour available each day. Brendan and Maeve believe that because of the health consciousness
of their potential clientele they will sell at least three fish meals for every two beef meals.
However, they also believe that at least 10% of their customers will order beef meals. The profit
from each fish meal will be approximately €12, and the profit from a beef meal will be about
€16.
a) Formulate a linear programming model for Brendan and Maeve that will help them
estimate the number of meals they should prepare each night to maximise the total
profit.
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