Question 2.55

2.55 Production costs for cell phone batteries

A company manufactures batteries for cell phones. The overhead expenses of keeping the factory operational for a month—even if no batteries are made—total $500,000. Batteries are manufactured in lots (1000 batteries per lot) costing $7000 to make. In this scenario, $500,000 is the fixed cost associated with producing cell phone batteries and $7000 is the marginal (or variable) cost of producing each lot of batteries. The total monthly cost y of producing x lots of cell phone batteries is given by the equation

  1. Draw a graph of this equation. (Choose two values of x, such as 0 and 20, to draw the line and a third for a check. Compute the corresponding values of y from the equation. Plot these two points on graph paper and draw the straight line joining them.)
  2. What will it cost to produce 15 lots of batteries (15,000 batteries)?
  3. If each lot cost $10,000 instead of $7000 to produce, what is the equation that describes total monthly cost for x lots produced?