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A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Solution Doll houses = x Furniture = y Labor: It takes 3 hours to make one x, so the total labor for making all of them is 3x hours. It takes 8 hours to make one y, for a total labor of 8y hours. Those added together must be less than or equal to 400 hours. 3x + 8y <= 400 Production Capacity: You can only make 100 items total a week, so you add the x and y and they must be less than or equal to 100. x + y <= 100 Requirements: You must have at least 20 of x made each week: x >= 20 And you must have at least 10 of y made each week: y >= 10 NOTE: >= means \"greater than or equal to\" <= means \"less than or equal to\" So, you need to graph these four inequalities: x >= 20 y >= 10 3x + 8y <= 400 x + y <= 100 .

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- A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Solution Doll houses = x Furniture = y Labor: It takes 3 hours to make one x, so the total labor for making all of them is 3x hours. It takes 8 hours to make one y, for a total labor of 8y hours. Those added together must be less than or equal to 400 hours. 3x + 8y <= 400 Production Capacity: You can only make 100 items total a week, so you add the x and y and they must be less than or equal to 100. x + y <= 100 Requirements: You must have at least 20 of x made each week: x >= 20 And you must have at least 10 of y made each week: y >= 10 NOTE: >= means "greater than or equal to" <= means "less than or equal to" So, you need to graph these four inequalities: x >= 20 y >= 10 3x + 8y <= 400 x + y <= 100