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. 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.

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.  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.

pfenn1 · Answer

Let x represent the number of workers and y represent the number of units manufactured.  We know from the first statement above that $$100 \le x \le 200$$and $$y \ge 3000$$Total daily cost C will be the daily cost per worker times the number of workers and the cost to manufacture 1 unit times the number of units.  Can you write the equation for that?