Aidan LeMay, Zack Ennen, Jakob Stokosa, and Nick Martinez Wallets Aidan LeMay, Zack Ennen, Jakob Stokosa, and Nick Martinez

Relationship between Defining the Variables and the Problem Situation A student is making two types of wallets out of duct tape. She is going to make a tri-fold wallet and a bi-fold wallet. The tri-fold wallet takes 1 hour to finish and the bi-fold wallet takes ½ hour to finish. Each tri-fold wallet costs $1 to make and each bi-fold wallet cost $0.75 to make. The tri-fold wallet sells for $10 and the bi-fold wallets sell for $8. If the student has at most $24 to purchase materials and no more than 20 hours throughout the week to make wallets, what combination of the ti-fold and bi-fold wallets should she make and sell to maximum profit? X= tri-fold wallet amount Y= bi-fold wallet amount

Relationship between the Problem Situation and the System of Linear Inequalities A student is making two types of wallets out of duct tape. She is going to make a tri-fold wallet and a bi-fold wallet. The tri-fold wallet takes 1 hour to finish and the bi-fold wallet takes ½ hour to finish. Each tri-fold wallet costs $1 to make and each bi-fold wallet cost $0.75 to make. The tri-fold wallet sells for $10 and the bi-fold wallets sell for $8. If the student has at most $24 to purchase materials and no more than 20 hours throughout the week to make wallets, what combination of the ti-fold and bi-fold wallets should she make and sell to maximum profit? Tri-fold: X≥0 Hours: 1 X+1/2Y≤20 Bi-fold:Y≥0 Cost: 1X+.75Y≤24

Optimal Solution To Problem Situation (Maximization Of Profit) Relationship: Satisfies the hours requirement (1X+1/2Y≤20) at 1(12)+1/2(16)≤20 as well as the cost restriction (1X+.75Y≤24) at 1(12)+.75(16)≤24. Explanation: If 12 trifold wallets at $10 and 16 bifold wallets at $8 are sold, then the profit will be $248. This satisfies both requirements, because the hours are about 12 and it will only cost $24. The point (12, 16) is the highest cornerpoint of the feasible region.

Closing The problem required us to calculate the maximum profit for selling duct tape wallets, which cost $1 to make a trifold wallet and $0.75 to make a bifold wallet. The cost restriction was $24. It takes 1 hour to make a trifold and 30 minutes (.5 hours) to make a bifold. Her limit is 20 hours. Finally, the bifold sells for $10, and the trifold for $8. The problem required us to calculate the maximum cost. We found that the coordinate (12, 16), as in 12 trifold and 16 bifold, satisfies the equation because it produces a cost of $24, a time of 12.03 (rounded to 13) hours, and produces a profit of $248