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Question 27878: Please help. I am terrible at setting up word problems.
A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities.
Answer by bmauger(101)   (Show Source):
You can put this solution on YOUR website! You need to graph each line to create a picture of this inequality. From the problem story "require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week" we are told explicitly that
and
We are also told that the production capacity is 50 items per week. So that means that the total of x & y can't exceed 50. Or  rewritting for y:
We're also given a production limit based on hours of labor. "The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week..." This is giving us a conversion for playhouses into man hours, and a total limit. Because it takes 12 hours per standard playhouse, the total number of hours constructing playhouses will be 12x. (Example, if they build 5 standards, it will take 12*5=60 hours). Following the same logic, it will take 20y hours to build deluxes. So the total labor hours involved are 12x+20y and they can't exceed 800, so we can write  Solving again for y, we get:
Now simply graph these 4 inequalities (sorry, the graphing program won't shade inequalities, but you get the idea). The possible scenarios are represented by the trapezoid formed by the 4 lines.
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