# Carmen's Origami Creations uses brown, green, orange, and yellow paper to createcenterpieces for Thanksgiving tables. A ower basket uses 10 brown papers, 15 greenpapers, 10 orange papers, and 5...

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.)

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### 1 Answer

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.)