Question

Plz help 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

a.
15 roast beef
15 chicken
c.
12 roast beef
18 chicken
b.
24 roast beef
6 chicken
d.
10 roast beef
20 chicken

Answer 1

The answer is a.

15 roast beef
15 chicken

Answer 2

Option A is the right answer.

Explanation:

Given information is:

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.

If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes.

Let x represent the roast beef sandwiches.

Let y represent the chicken salad sandwiches.

The system of equations becomes:

`x+y=30` or
`x=30-y` ..... (1)

`5x+3y=120` ....(2)

Substituting (1) in (2)

`5(30-y)+3y=120`

`150-5y+3y=120`

`150-2y=120`

`150-120=2y`

`2y=30`

y = 15

As
`x=30-y` so,
`x=30-15`

x = 15

Now we will see the profit;

P =
`(3*15)+ (2*15)=45+30=75` dollars

Therefore, 15 roast beef sandwiches and 15 chicken salad sandwiches should be prepared to maximize the profit.

Hence, the answer is option A.