Suppose a factory can have no more than 200 workers on a shift, but must have at least 100 and must manufacture at least 3000 units at minimum cost. The managers need to know how many workers should be on a shift in order to produce the required units at minimal cost. Let “x” represent the number of workers and y represent the number of units manufactured.
1. Write an inequality for the number of manufactured units at minimum cost.
2. Would the above inequality be drawn with a solid or dashed line?
3. Graph the region formed by the constraints given in the problem and find all vertices of t
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4. What quadrant should you place your graph and why?
5. If the cost per worker is $50 per day and the cost to manufacture 1 unit is $100, write an expression representing the total daily cost C.
6. Using the points given above, what is the minimum cost?
7. How many workers should be on a shift in order to produce the required units at minimal cost?