TA Manufacturing Company produces transmission parts and sells to different

Auto Repair shops $6000$ units per year. ATA can produce these transmission parts at a rate of $70$ units$/$hour$.$

Machine setup time to produce these parts is $3\mathrm{.}5$ hours. Labor for this work is estimated at a rate of

$$60/$hour$,$ and manufacturing plant idle time during setups is estimated to cost the firm around $$220$ per

hour in lost profit. ATA uses a $22\%$ annual interest rate for holding cost estimation. Each transmission part

costs ATA $$25$ to produce; they are sold for $$55$ each to auto repair shops. ATA works one shift of ten$-$

hours per day Monday through Saturday.

a$)(7$ points$)$ What is the optimal production quantity for this transmission part that minimizes inventory

related costs?

b$)(6$ points$)$ What is the maximum expected level of on$-$hand inventory for these transmission parts?

c$)(6$ points$)$ What is the uptime and down time during each production cycle?

d$)(6$ points$)$ What is the total annual expected cost for the optimal production policy? What is the

expected annual profit