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?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.CR: Chapter Review
Problem 70E: A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three...
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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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