A multi$-$product manufacturing line involves setups between products, and can produce

component WX$93$ at an average rate of $600$ per hour. The components use materials

valued at $$0\mathrm{.}02$ each. A production day is $8$ hours. Production setup time is $3$ hours, and

inventory holding costs are estimated at $25\%$ annualized. The production line is operated

by one worker, who is paid $$50/$hour$.$

a$.$ If the demand is $17000$ per week, prepare a production plan for WX$93$ to trade$-$

off setup and inventory costs. Also calculate the total annual setup and inventory

costs for WX$93.$

b$.$ Four weeks into production, you are told that "because of sudden popularity of a

product in which WX$93$ is used, the new demand is $34000$ per week". What

considerations are necessary to make this work?