Acc GPS AA / Geometry Name: ______________Pd: _____ Linear Programming Worksheet For each problem: a) Identify the functions to be maximized or minimized b) Define your variables c) Write an objective function statement using your variables d) Write a system of linear inequalities that represent the constraints e) Graph the feasibility region f) Using the vertices from your graph, determine the max/min value and answer the question 1. A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a large bookcase and 2 hours to make a small one. The profit on a large bookcase is $35 and on a small bookcase is $20. The carpenter can spend only 32 hours per week making bookcases and must make at least 2 of the large and at least 4 of the small each week. How many small and large bookcases should the carpenter make to maximize his profit? What is his profit? 2. A small town is trying to establish a transportation system of large and small vans. It can spend no more than $100,000 for purchasing both sizes of vehicles and no more than $500 per month for maintenance. The town can purchase a small van for $10,000 and maintain it for $100 per month. The large vans cost $20,000 each and can be maintained for $75 per month. Each large van carries a maximum of 15 passengers and each small van carries a maximum of 7 passengers. Find the maximum number of passengers the transportation system can handle given the constraints. How many large and small vans will they need to maximize the number of passengers it can service?

3. A ski company makes two types of skis and has a fabrication and a finishing department. A pair of downhill skis requires 6 hours to fabricate and 1 hour to finish. A pair of cross-country skis requires 4 hours to fabricate and 1 hour to finish. The fabricating department has 108 hours of labor available per day. The finishing department has 24 hours of labor available per day. The company makes a profit of $40 on each pair of downhill skis and $30 on each pair of cross-country skis. How many of each type should the manufacturer produce to maximize his profit? What is the max profit? Scale: Let each square represent 3 units 4. An office manager is purchasing file cabinets and wants to maximize storage space. The office has 60 sq. ft. of floor space for the cabinets and $600 in the budget to purchase them. Cabinet A requires 3 sq. ft. of floor space, has a storage capacity of 12 cubic ft., and costs $75. Cabinet B requires 6 sq. ft. of floor space, has a storage capacity of 18 cubic ft. and costs $75. How many of each cabinet should the office manager buy? 5. You are stenciling wooden boxes to sell at a fair. Stenciling takes 2 hours for a small box and 3 hours for a large box. Profit for a small box is $10 and for a large is $20. If you have no more than 30 hours available to but want at least 12 boxes to sell, how many of each size box should you sell to maximize your profit? Scale: Let each square represent 2 units