Intermediate Algebra Linear Programming Name___________________________Hr_____ 1. Emilio has a small carpentry shop in his basement to make bookcases. He makes two sizes, large and small. His profit on a large bookcase is $80, and his profit on a small bookcase is $50. It takes Emilio 6 hours to make a large bookcase and 2 hours to make a small one. He can spend only 24 hours each week on his carpentry work. He must make at least two of each size each week. What is the maximum weekly profit? 2a. _______________________ a. Translate the constraints into a system of inequalities. Let L = the _______________________ number of large bookcases and S = _______________________ the number of small bookcases. _______________________ b. Write an optimization equation to represent the profit per month. c. Use the graph at right to find the feasibility region. d. Find the vertices of the feasiblity region. e. Apply the Fundamental Theorem of Linear Programming and interpret the results. (Check the points at each vertex of the feasibility region to see which results in the greatest profit.) 2b. _______________________ 2d. _______________________ _______________________ _______________________ _______________________ 2e. Most profit from: _______________________ Profit is: _______________________ 2. Jocelyn’s Jewelry Store makes rings and pendants. Every week the staff uses at most 500 grams of metal and spends at most 80 hours making jewelry. It takes 5 grams of metal to make a ring and 20 grams of metal to make a pendant. Each ring takes 1.5 hours to make and each pendant takes 1 hour. If the profit on each ring is $90 and the profit on each pendant is $40, how many of each should be produced to maximize profit? Most profit from: _______________________ Profit is: _______________________ 3. Nike decided to abandon shoes for a while and just make socks and t-­‐shirts. Each package of socks gives Nike a profit of $12, and each t-­‐shirt gives them $18 in profit. Over in Taiwan, each package of socks takes two minutes of cutting time and 6 minutes of sewing time. The t-­‐shirts take 3 minutes of cutting time and 3 minutes of sewing time. If the sewing machine is available 18 minutes per hour, and the cutting mathine is available 12 minutes per hour, what mix of socks and t-­‐shirts will give Nike the most profit? Most profit from: _______________________ Profit is: _______________________