1 Graph the feasible region for the following

1. Graph the feasible region for the following constraints. x ≥ -2 y≤ 1 y ≥ 1/2 x – 2 y ≤ -2 x +3 3 -4 Linear Programming

2. Graph the feasible region for the following constraints. x≥ 0 y ≥ 1. 5 2. 5 x + 5 y ≤ 20 2 x + 2 y ≤ 12 3 -4 Linear Programming

3. Gillian is planning a green roof that will cover up to 600 square feet. She will use two types of plants: blue lagoon sedum and raspberry red sedum. Each blue lagoon sedum will cover 1. 2 square feet. Each raspberry red sedum will cover 2 square feet. Each plant costs $2. 50, and Gillian must spend less than $1000. Write the constraints, and graph the feasible region. 3 -4 Linear Programming

3. One of Gillian's priorities for the green roof is to help control air pollution. To do this, she wants to maximize the amount of carbon dioxide the plants on the roof absorb. Use the carbon dioxide absorption rates and the data from example 1 to find the number of each plant Gillian should plant. Blue Lagoon 1. 4 lb of CO 2 per year, Raspberry Red 2. 1 lb of CO 2 per year x≥ 0 y≥ 0 1. 2 x + 2 y ≤ 600 2. 50 x + 2. 50 y ≤ 1000 3 -4 Linear Programming

3. x≥ 0 y≥ 0 1. 2 x + 2 y ≤ 600 2. 50 x + 2. 50 y ≤ 1000 C = 1. 4 x + 2. 1 y 3 -4 Linear Programming

X= Y= 4. Brad is an organizer of the Bolder Boulder 10 K race and must hire workers for one day to prepare the race packets. Skilled workers cost $60 a day and students cost $40 a day. Brad can spend no more than $1440. He needs at least 1 skilled worker for every 3 students, but only 16 skilled workers are available. Skilled workers can prepare 25 packets per hour and students can prepare 18 packets per hour. Find the number of each type of worker that Brad should hire to maximize the number of packets produced. 3 -4 Linear Programming

X = number of students Y = number of skilled workers 4. Brad is an organizer of the Bolder Boulder 10 K race and must hire workers for one day to prepare the race packets. Skilled workers cost $60 a day and students cost $40 a day. Brad can spend no more than $1440. He needs at least 1 skilled worker for every 3 students, but only 16 skilled workers are available. Skilled workers can prepare 25 packets per hour and students can prepare 18 packets per hour. Find the number of each type of worker that Brad should hire to maximize the number of packets produced. 3 -4 Linear Programming

4. x≥ 0 y≥ 0 40 x + 60 y ≤ 1440 y ≥ 1/3 x y ≤ 16 P = 18 x + 25 y 3 -4 Linear Programming

3 -4 Linear Programming Homework