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1. A company manufactures 4 products. They have the following restrictions: Available volume: 180 lb. Available storage space: 230m3 In order to finish each product they need the following: Product 1 2 3 4 Raw materials lbs. / unit 2 2 1.5 4 Space m3 2 2.5 2 1.5 Profit $/unit 5 6.5 5 5.5 - What is the linear programing model to maximize the profits to this case? - What is the optimal solution? 2. - A company produces two types of machinery, one is top quality and the other one standard. Each machine needs a different manufacturing technique. The top quality machine needs 18 hours of labor, 9 hours for testing and generates profits for $400. The standard machine needs 3 hours of labor and 4 hours of testing generating profits for $100. There is 900 hours of labor available and 600 hours available for testing. The forecast for the standard machine is up to 120 units. How many standard and top quality machines they need to produce in order to maximize profits? 3. - A company produces two types of cars: small and medium size. The production of each car requires a certain amount of raw materials and labor as it shows on the following table: Raw material quantity Labor (hours) Profit $ Small size 50 20 4,500 Medium size 10 20 5,500 Total available 15,000 9,000 There are 15,000 units of raw material and 9,000 hours of labor available. The forecast shows that they can sell up to 300 medium size cars. Determine the amount of cars of each type to maximize the total profit

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Let P = profit, w = # product 1, x = # product 2, y = # product 3, z=# product 4

Max P = 5w + 6.5x + 5y + 5.5z
2w+2x+1.5y+4z <= 180 (raw materials constraint)
2w+2.5x+ 2y+ 1.5z <= 230 (Space constraint)
w,x,y,z >=0 (non negativity constraints)...
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