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A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, whereas the turkey special gives a profit of $3.10 per sandwich. The roast beef special uses two slices of bread and three slices of cheese. The turkey special uses two slices of bread and four slices of cheese. The deli has 120 slices of bread and 160 slices of cheese available for the specials. The deli wants to maximize its profit selling sandwiches. Let x represent the number of roast beef specials and y represent the number of turkey specials.

What are the constraints for the problem?

A. 2x+2y ≤ 120
3x+4y≤160
2.3x≥ 3.1y

B. 2x+2y ≤ 120
3x+4y≤160
x≥0
y≥0

C. 2x+3y≤ 120
2x+4y≤ 160
x≥0
y≥0

D. 2x+3y≤120
2x+4y≤160
x≥0
y≥0

Respuesta :

livefranoor5w13
F (x,y) = 2.30x + 3.10y

The constraints are described with the following inequalities:
2x + 2y < = 120
3x + 4y < = 160
The corner points are: ( 0, 40) and (40/0.75, 0)
F (0,40) = 3.10 * 40 =$124
F (40/0.75,0) = (40/0.75) * 2.30 = $122.67
To maximize the profit they should sell 40 Turkey Specials.
So your answer should be C.

Answer:

The required constraints are:

[tex]2x+2y\leq120[/tex]

[tex]3x+4y\leq160[/tex]

[tex]x\geq0[/tex]

[tex]y\geq0[/tex]

Step-by-step explanation:

Consider the provided information.

Let, x is the number of roast beef specials and y is the number of turkey specials.

The profit from roast beef special is $2.30 per sandwich, the profit from turkey special is $3.10 per sandwich.

The profit function will be:

[tex]P(x,y)=2.3x+3.10y[/tex]

The bread slices constraint will be:

The roast beef special uses two slices of bread and the turkey special uses two slices of bread. The deli has 120 slices of bread.

[tex]2x+2y\leq120[/tex]

The cheese slices constraint will be:

The roast beef special uses three slices of cheese and the turkey special uses four slices of cheese. The deli has 160 slices of cheese.

[tex]3x+4y\leq160[/tex]

The number of both sandwiches must be greater than zero.

Thus, the constraint will be:

[tex]x\geq0[/tex]

[tex]y\geq0[/tex]

Therefore, the required constraints are:

[tex]2x+2y\leq120[/tex]

[tex]3x+4y\leq160[/tex]

[tex]x\geq0[/tex]

[tex]y\geq0[/tex]

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