Question

Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.
The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.

Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?

Select each correct answer.



(11, 14)

(10, 12)

(12, 10.5)

(15, 11)

(11, 9)

Answer 1

Let

x-------> represents the poodle’s body length

y-------> represents the shoulder height

Constraints

$10\ in \leq y \leq 15\ in$ --------> constraint A

$x \leq 16\ in$ --------> constraint B

$y \leq x+1$ --------> constraint C  

Using a graphing tool

see the attached figure

The solution is the shaded area

we know that

If a pair ordered is a solution for a successful poodle measurement

then

the pair ordered meet all the constraints

Let's check each case to determine the solution to the problem

Replace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solution

Case A) $(11,14)$  

constraint A

$10\ in \leq 14 \leq 15\ in$ ------> is true

constraint B

$11 \leq 16\ in$ --------> is true

constraint C

$14 \leq 11+1$

$14 \leq 12$ -------> is not true

therefore

the pair  $(11,14)$ does not meet all constraints

Case B) $(10,12)$  

constraint A

$10\ in \leq 12 \leq 15\ in$ ------> is true

constraint B

$10 \leq 16\ in$ --------> is true

constraint C

$12 \leq 10+1$

$12 \leq 11$ -------> is not true

therefore

the pair  $(10,12)$  does not meet all constraints

Case C) $(12,10.5)$  

constraint A

$10\ in \leq 10.5 \leq 15\ in$ ------> is true

constraint B

$12 \leq 16\ in$ --------> is true

constraint C

$10.5 \leq 12+1$

$10.5 \leq 13$ -------> is true

therefore

the pair  $(12,10.5)$  meets all constraints

Case D) $(15,11)$  

constraint A

$10\ in \leq 11 \leq 15\ in$ ------> is true

constraint B

$15 \leq 16\ in$ --------> is true

constraint C

$11 \leq 15+1$

$11 \leq 16$ -------> is true

therefore

the pair $(15,11)$ meets all constraints

Case E) $(11,9)$  

constraint A

$10\ in \leq 9 \leq 15\ in$ ------> is not true

constraint B

$11 \leq 16\ in$ --------> is true

constraint C

$11 \leq 15+1$

$11 \leq 16$ -------> is true

therefore

the pair  $(11,9)$    does not meet all constraints

therefore

the answer is

$(12,10.5)$

$(15,11)$

Answer 2

The first one, the fourth one, and the middle one