Q12. - Algebra 2

Question

12.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 of the club plans to sell the canvas bags at a project of 20 and the leather bags at a project of 35 each, write a function for the total project of the bags.

Step-by-Step Solution

Answer

The function for the total project on the bag is $f(c,l)=20c+35l$

Step 1-form an in equation from the given detail

Total leather $=56$yards

Total canvas $=104$

Now, leather constraint : $c+3l\le 56$

Canvas constraint: $4c+2l\le 104$

Where$l\ge 0$ and $l\ge 0$

Step 2-Mention the given date

‘C’ and ‘l’ are the number of canvas tote and the number of leather tote project of each canvas bags is 20 and project of leather bags is 35 let $f(c,l)$ is the function of project.

Step 3- By applying the concept of in equation, formed the function for the total project on the bag

Let $f(x,y)$ be the function for the total project 

$\therefore f(c,l)=20c+35l$