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)
Accepted Solution
A:
Letx-------> represents the poodle’s body lengthy-------> represents the shoulder heightConstraints[tex]10\ in \leq y \leq 15\ in[/tex] --------> constraint A[tex]x \leq 16\ in[/tex] --------> constraint B[tex]y \leq x+1[/tex] --------> constraint C Using a graphing toolsee the attached figureThe solution is the shaded areawe know thatIf a pair ordered is a solution for a successful poodle measurementthen the pair ordered meet all the constraintsLet's check each case to determine the solution to the problemReplace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solutionCase A) [tex](11,14)[/tex] constraint A[tex]10\ in \leq 14 \leq 15\ in[/tex] ------> is trueconstraint B[tex]11 \leq 16\ in[/tex] --------> is trueconstraint C[tex]14 \leq 11+1[/tex][tex]14 \leq 12[/tex] -------> is not truethereforethe pair [tex](11,14)[/tex] does not meet all constraintsCase B) [tex](10,12)[/tex] constraint A[tex]10\ in \leq 12 \leq 15\ in[/tex] ------> is trueconstraint B[tex]10 \leq 16\ in[/tex] --------> is trueconstraint C[tex]12 \leq 10+1[/tex][tex]12 \leq 11[/tex] -------> is not truethereforethe pair [tex](10,12)[/tex] does not meet all constraintsCase C) [tex](12,10.5)[/tex] constraint A[tex]10\ in \leq 10.5 \leq 15\ in[/tex] ------> is trueconstraint B[tex]12 \leq 16\ in[/tex] --------> is trueconstraint C[tex]10.5 \leq 12+1[/tex][tex]10.5 \leq 13[/tex] -------> is truethereforethe pair [tex](12,10.5)[/tex] meets all constraintsCase D) [tex](15,11)[/tex] constraint A[tex]10\ in \leq 11 \leq 15\ in[/tex] ------> is trueconstraint B[tex]15 \leq 16\ in[/tex] --------> is trueconstraint C[tex]11 \leq 15+1[/tex][tex]11 \leq 16[/tex] -------> is truethereforethe pair [tex](15,11)[/tex] meets all constraintsCase E) [tex](11,9)[/tex] constraint A[tex]10\ in \leq 9 \leq 15\ in[/tex] ------> is not trueconstraint B[tex]11 \leq 16\ in[/tex] --------> is trueconstraint C[tex]11 \leq 15+1[/tex][tex]11 \leq 16[/tex] -------> is truethereforethe pair [tex](11,9)[/tex] does not meet all constraintsthereforethe answer is[tex](12,10.5)[/tex][tex](15,11)[/tex]