$(15)$ Two products are manufactured on the same production line. Product A has setup cost

of $$750$ and per$-$period inventory carrying cost of $$3.$ Product $B$ has a setup cost of $$600$ and

a per$-$period inventory carrying cost of $$4.$ The production rate for both products is $200$ per

period. Product A has an average weekly demand of $82,$ and Product $B$ has an average

weekly demand of $95.$

a$.(5)$ What is the optimal joint production cycle time for the two products?

b$.(10)$ Round the joint optimal cycle time to the nearest integer. How much slack time

is available for setup times, failures, etc. with this cycle time?