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8.7 Applications of Linear Programming

8.7 Applications of Linear Programming. Linear Programming is a tool for solving real world problems It is important to interpret the information correctly. *Groups of 3:

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8.7 Applications of Linear Programming

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  1. 8.7 Applications of Linear Programming

  2. Linear Programming is a tool for solving real world problems It is important to interpret the information correctly. *Groups of 3: Each member is responsible for 1 job each during the problem. You can work together, but if it is your job, you are responsible for writing the information on your whiteboard. On the next problem, we rotate jobs, so everyone has a chance at each job. Job 1: Writing the equations (on whiteboard) Job 2: Graph on Desmos & find vertices of feasible region (put on whiteboard) Job 3: Evaluate the vertices in optimization function. Find answer. Write answer on whiteboard in acomplete sentence.

  3. Ex 1) A supermarket wants to purchase automatic hand-held price labelers. The first type can label 7 items per minute & costs $5. The second can label 10 items per minute & costs $6. The manufacturer can supply at most 60 of type A and 45 of type B. The supermarket wants to limit its costs to $420. Determine how many of each type of labeler should be purchased to maximize the number of items that can be processed. • Let x = type A cost: 5x+ 6y≤ 420 • y = type B x ≤ 60, x ≥ 0 • y ≤ 45, y ≥ 0 • Max # processed: P = 7x + 10y • The supermarket should buy 30 of type A & 45 of type B supply restrictions

  4. Ex 2) A nutritionist is requested to devise a formula for a base for an instant breakfast meal. The breakfast must contain at least 12g protein and 8g carbohydrates. A tablespoon of protein powder made from soybeans has 5g protein & 2g carbohydrates. A tablespoon of protein powder made from milk solids has 2g protein & 4g carbohydrates. Soybean protein powder costs $0.70 per tablespoon and milk protein powder costs $0.30 per tablespoon. Determine the number of tablespoons of each type of protein powder that should be used as the base for this breakfast to meet the given requirements and minimize the cost. • Let x = soybean protein: 5x+ 2y ≥ 12, x ≥ 0 • y = milk carbs: 2x+ 4y≥ 8, y ≥ 0 • Cost (minimize): C = .70x + .30y • The breakfast should have 2 tbsp soybean & 1 tbsp milk powder

  5. Ex 3) A manufacturer makes two types of picnic tables, deluxe & standard. The deluxe table takes 6 hours to build & 1 hour to finish. The standard table takes 4 hours to build and 2 hours to finish. The manufacturer can devote at most 120 hours per week to building and 40 hours per week to finishing. The profit on the deluxe table is $50 and on the standard table, $36. Find how many of each type of table that should be produced to maximize the profit. • Let x = deluxe build: 6x+ 4y ≤ 120, x ≥ 0 • y = standard finish: x+ 2y ≤ 40, y ≥ 0 • Profit (max): P= 50x + 36y • The manufacturer should make 10 deluxe & 15 standard picnic tables

  6. Homework #807 Pg428 #1, 3, 12, 21, 22–24, 33

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