The manager for quality control at a tool company has determined that quality control

costs for the firm have two components, an inspection cost and a production repair cost (both in $thousands). Both costs are functions of the number of inspections performed

during the manufacturing process. The inspection cost is given by Ci= 4x, , where x is the

number of inspections performed each month. Monthly production repair costs decrease with the number of inspections, which eliminate defective tools before they are sold,

according to (Cr= 64/x) .Total quality control costs are the sum of these two functions.

1. If the manager wishes to minimize the firm's total quality control costs, what number of inspections is optimal?
2. How do you know the number of inspections you found minimizes total quality control costs?
3. What's the minimized level of quality control costs?