please help me with this question Please show steps and expl

please help me with this question. Please show steps and explain your reasoning via equations

The following variables are defined for a typical metal cutting operation: M =machine and operator charge rate ($/hour) N_T = number of tools used (number of tools batch) N_b = number of parts in a batch (number of parts/batch) t_L = part loading/unloading time (hour/part) t_m = machining time (hours/part) t_c = tool change time for worn tools (hours/tool) C_t = tool cost ($/tool) The total production cost per part C_pr can best be described as: Mt_L + Mt_m + M(N_T/N_b)t_c + (N_T/N_b) C_t M(N_b t_L + N_b t_c + N_T t_m) + N_T C_t M(N_b t_L + N_b t_m + N_T t_c) + N_T C_T Mt_L + Mt_m + (N_t/N_b)t_c + (N_T/N_b) C_t

Solution

Answer -Option C

Total Cost of machining = Tooling cost+Machining cost+ Operator cost+ cost associated with tool changing time

Also we can say machining cost= cost associated with loading and unloading of parts + machining cost of parts/batch+cost associated during tool changing+total cost of tools

hence

the cost associated with loading and unloading of th part into the machine= M*Nb*tc

Machining cost of each part/batch = M*Nb*tm

cost associated during tool changing = M*Nt*Tc

Total cost of tools used for machining = Nt*Ct

so the Total cost will be =M(Nb*tc+Nb*tm+Nt*tc) + Nt*Ct