A lunch counter sells two types of sandwiches: roast beef and chicken salad. It earns a profit of $2 for each chicken salad sandwich it sells and $3 for each roast beef sandwich. There is only enough bread to make up to 30 sandwiches, and it only has enough roast beef to make a maximum of 20 roast beef sand- wiches. It takes 10 minutes to prepare each chicken salad sandwich and 4 min- utes to prepare each roast beef sandwich. If the maximum amount of time the lunch counter has to prepare sandwiches is 4 hours (240 minutes), how many of each type of sandwich should be prepared to maximize profit?
A lunch counter sells two types of sandwiches: roast beef and chicken salad. It earns a profit of $2 for each chicken salad sandwich it sells and $3 for each roast beef sandwich. There is only enough bread to make up to 30 sandwiches, and it only has enough roast beef to make a maximum of 20 roast beef sand- wiches. It takes 10 minutes to prepare each chicken salad sandwich and 4 min- utes to prepare each roast beef sandwich. If the maximum amount of time the lunch counter has to prepare sandwiches is 4 hours (240 minutes), how many of each type of sandwich should be prepared to maximize profit?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter6: Systems Of Linear Equations And Inequalities
Section6.1: Graphing Systems Of Equations
Problem 59PFA
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Transcribed Image Text:A lunch counter sells two types of sandwiches: roast beef and chicken salad. It
earns a profit of $2 for each chicken salad sandwich it sells and $3 for each
roast beef sandwich. There is only enough bread to make up to 30 sandwiches,
and it only has enough roast beef to make a maximum of 20 roast beef sand-
wiches. It takes 10 minutes to prepare each chicken salad sandwich and 4 min-
utes to prepare each roast beef sandwich.
If the maximum amount of time the lunch counter has to prepare sandwiches is
4 hours (240 minutes), how many of each type of sandwich should be prepared
to maximize profit?
Your solution written in the sketchpad below should provide the following:
⚫ the system of inequalities that represents the constraints (given and
implied) in the problem;
⚫ a graph of the system of inequalities representing the constraints;
⚫ the locations of the critical points of the feasible region and any
calculations necessary to determine them;
⚫ the objective function and calculations made using it; and
⚫ a complete statement of the solution that answers the question asked in
the problem.
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