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Algebra 2A Unit 2 05 Evaluate Graded Assignment Directions: Use the table and information below to answer questions 1 through 7. For help, revisit the lesson, especially the page "Explain: Linear Programming" or contact your instructor before submitting this assignment. Let's put your knowledge of linear programming to the test. Recall in the video that Mr. Green needed help figuring out how many plants to buy in order to maximize profit during the Bastille Day Sale. Here is the information that Mr. Green provided us: \begin{tabular}{|c|c|c|c|} \hline Type of Plant & Square Footage & Gallons of Soil & Cost \\ \hline Giant Potted & 7 & 14 & $\$ 14$ \\ \hline Hanging Basket & 4 & 2 & $\$ 5$ \\ \hline \end{tabular} - Mr. Green has 168 square feet of space available, 210 gallons of soil and a budget of $\$ 252$. - Mr. Green sells each giant potted plant for $\$ 28$ and sells each hanging plant for $\$ 8$. - Goal: Write a system of inequalities and determine which combination of plants will maximize profit for Mr. Green. 1. Define the variables ( 10 points: 5 for each) 2. Write the objective function for profit. (10 points) 3. Write a system of linear inequalities that represents the problem's restrictions ( 20 points: 4 points for each inequality)

Algebra 2A 66505 05 Evaluate Graded Assignment 4. Graph the system of inequalities ( 25 points: 5 points for each inequality) 5. Find the vertices of the region that contains the solutions to the system of linear inequalities (10 points: 2 points for each vertex) 6. Test the coordinates of each vertex in the objective function to find the one that gives the maximum profit (15 points: 3 points for testing each vertex)

7. State the solution in terms of the variables (10 points) University of Texas at Austin UT High School