Carmen's Origami Creations uses brown, green, orange, and yellow paper to create
centerpieces for Thanksgiving tables. A ower basket uses 10 brown papers, 15 green
papers, 10 orange papers, and 5 yellow papers, while a cornucopia uses 20 brown
papers, 10 green papers, 15 orange papers, and 3 yellow papers. Carmen currently
has 500 brown papers, 300 green papers, 300 orange papers, and 100 yellow papers
available. Give a system of inequalities that describes the feasible combinations of
ower baskets and cornucopias that Carmen can make using the supplies on hand.
Be sure to indicate which type of paper corresponds to each inequality. (Note: You
need not graph the feasibility region.)
Let b be the number of ower baskets and c the number of cornucopias.
(1) Brown paper: `10b+20clt=500`
(10 brown papers for each basket and 20 papers for each cornucopia; the total of brown paper is 500)
(2) Green paper: `15b+10clt=300`
(3) Orange paper: `10b+15c<=300`
(4) Yellow paper: `5b+3c<=100`
(5) "Natural constraints": `b>=0,c>=0` (You cannot create a negative number of baskets.)