Question

3. The manager for quality control of a tool company has determined that quality control costs for the firm have two components, an inspection cost and a production repair cost. Both costs are a function of the number of inspections performed during the manufacturing process. The inspection cost per unit of production is given by C, = 3X, where X is the number of inspections performed. Production repair cost per unit of production is given as CR=27 If the quality control manager wishes to minimize the firm's quality control costs per unit of production, C, +CR, what number of inspections is optimal? (Check the SOC.)

Answer 1

Minimize total cost , T = CI + CR

T= 3X + 27/X

So FOC : dT/dX = 3 - 27/X^{​​​​​​2} = 0

1 = 9/X^{​​​​​​2}

X*= 3

So optimal number of inspection = 3

SOC : d²T/dX^{​​​​​2} = +54/X^{​​​​​​3} > 0

This SOC is satisfied