A lunch counter sells two types of sandwiches, roast beef and chicken salad. The profit on the sandwiches is $2 for chicken salad and $3 for roast beef. The amount of bread available is enough for 30 sandwiches. There are 2 hours available to prepare sandwiches. If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes, how many of each type of sandwich should be prepared to maximize the profit? Assume all sandwiches get sold

Question

Mathematics

Isabel Jacobson

18 November, 09:27

A lunch counter sells two types of sandwiches, roast beef and chicken salad. The profit on the sandwiches is $2 for chicken salad and $3 for roast beef. The amount of bread available is enough for 30 sandwiches. There are 2 hours available to prepare sandwiches. If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes, how many of each type of sandwich should be prepared to maximize the profit? Assume all sandwiches get sold

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Answers (1)

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Jaycee Lee · Answer 1

For this case we define variables:

x: roast beef sandwiches

y: chicken salad sandwiches

We write the system of equations:

x + y = 30

5x + 3y = 120

Solving the system we have:

x = 15

y = 15

The profit is:

P = 3 * (15) + 2 * (15)

P = 75 $

Answer:

should be prepared to maximize the profit:

15 roast beef sandwiches

15 chicken salad sandwiches