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 the unbounded region. 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?

Question

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 the unbounded region.   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?