Q11. - Algebra 2

Question

11.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. List the co-ordinate of the vertices of feasible region

Step-by-Step Solution

Answer

The vertices of feasible region is$O(0,0),A(26,0),B(20,12)$ and $C(0,18.66)$

Step1Apply the concept of the formation of constraint

c=no of canvas tote bags

l=no of leather bags

Now, for each canvas tote bags they required 4 yard of canvas and 1 yard of leather, and for each leather bags they required 3 yard of leather and 2 yard of canvas

Step 2-Draw a graph of the given inequalities

We form 2 in equation$4c+2l\le 104$ and $c+3l\le 56$ where ‘c’ and ‘l’ are the quantity of canvas tote and leather respectively. Plot canvas along x-axis and leather tote along y-axis

Step 3-Find the common region and the vertices of the common region

From the graph we can see that the common region as feasible are bounded and quadrilateral in shape. OABC is a feasible region of vertices$o(0,0),A(26,0),B(20,12),C(0,18.66)$