Q13. - Algebra 2

Question

13.The students is the future Homemaker club are making canvas tote bag and leather tote bags for a money making project. They will line both type of tote bags with canvas and use leather for the handle of both bags .For the canvas tote bags, they need 4 yards of canvas and 1 yard of leather for the leather tote bags, they need 3 yard of leather and 2 yard of canvas their faculty advisor has purchased 56 yard of leather and 104 yard of canvas. Determine the number of canvas and leather, bags that they need to make for the maximum project.

Step-by-Step Solution

Answer

To make maximum project they need 20 canvas bags and 12 leather bag

Step 1-Identify the vertices of a feasible region and form a function for the total project

We have to vertices of the bounded region that is$(0,0),(26,0),(20,12)$ and$(0,18.66)$. The function for the total project is$f(c,l)=20c+35l$

Step 2-Now calculate the value of f ( c , l )

$\begin{array}{ccc}(c,l)& 20c+35l& f(c,l)\\ (0,0)& 20\left(0\right)+35\left(0\right)& 0\\ (26,0)& 20\times 26+35\times 0& 520\\ (20,12)& 20\times 20+35\times 12& 820\\ (0,18.66)& 20\times 0+35\times 18.66& 653.1\end{array}$

Step 3-Calculate the maximum value with corner points

From the above table we can see that the maximum project is$(20,12)$ that is the number of canvas bag is 20 and leather bag is 12.