Question

10.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. Draw the graph showing the feasible region.

Short answer

OABC is a feasible region of the given system of inequalities

Step-by-step solution

Step 1-Apply the concept of plotting a point on graph paper

Graph the inequalities, $c+3l\le 56$and$4c+2l\le 104$.Where c and ‘l’ are the quantities of canvas and leather tote respectively. We plot ‘c’ on the x-axis and ‘l’ on the y-axis

For, $c+3l\le 56$

$\begin{array}{cccc}c& 8& 20& -2\\ l& 16& 12& 18\end{array}$

For $4c+2l\le 104$

$\begin{array}{cccc}c& 26& 20& 16\\ l& 0& 12& 20\end{array}$

Step 2-Plot the corner point and draw the feasible region

Step 3-Find the common region of inequalities

From the graph we can see that the feasible region is a ABCO quadrilateral which is bounded region.