6.1.5 Linear Programming Review

Identify each of the following system of linear equations as having no solution, one solution, or infinitely many solutions.

 $2x+4y=14$  

 $6x+12y=42$  

• one solution

• no solutions

• infinitely many solutions

• two solutions

Tags

CCSS.8.EE.C.8B

Identify each of the following system of linear equations as having no solution, one solution, or infinitely many solutions.
 $12x+9y=8$  
 $4x+3y=5$  

• one solution

• no solutions

• infinitely many solutions

• two solutions

Tags

CCSS.8.EE.C.8B

Identify each of the following system of linear equations as having no solution, one solution, or infinitely many solutions.
 $6x+2y=9$  
 $2x-4y=2$  

• one solution

• no solutions

• infinitely many solutions

• two solutions

Tags

CCSS.8.EE.C.8B

Select an inequality that shows the constraint on the amount of apples Lexie has to make cobblers and pies.

• $2x+6y\le18$

• $6x+2y\le18$

• $4x+2y\le16$

• $2x+4y\le16$

Select an inequality that shows the constraint on the amount of flour Lexie has to make cobblers and pies.

• $2x+6y\le18$

• $6x+2y\le18$

• $4x+2y\le16$

• $2x+4y\le16$

1. Since Lexie can’t make a negative number of cobblers or pies, what additional constraints exist on our variables? Select all that apply.

• $x\le0$

• $x\ge0$

• $y\le0$

• $y\ge0$

Select the four constraints into the graphing calculator. What are the vertices of the feasible region? Select all that apply.

•  $\left(0,0\right)$  

•  $\left(0,8\right)$  

•  $\left(8,0\right)$  

•  $\left(4,0\right)$  

•  $\left(1,6\right)$  

Select an objective function that models the total profit from cobblers and pies.

• $P\left(x,y\right)=2x+3y$

• $P\left(x,y\right)=5x+6y$

• $P\left(x,y\right)=3x+2y$

• $P\left(x,y\right)=6x+5y$

Evaluate each vertex ordered pair in the profit function. What is the maximum profit?

• $\left(0,0\right)$

• $\left(0,8\right)$

• $\left(8,0\right)$

• $\left(4,0\right)$

• $\left(1,6\right)$