$($a$)$ If overtime costs only $$4$ per hour $($and all other parameters remain unchanged$),$ how much overtime should All$-$Balsa use?

$($b$)$ If each unit of bookcase $1$ sold for $$15\mathrm{.}50($and all other parameters are unchanged$),$ what will the optimal profit per week be $-$ or can you not tell without resolving the LP$?$

$($c$)$ What is the most All$-$Balsa should be willing to pay for another unit of raw material?

$($d$)$ If each worker were required $($as part of the regular workweek$)$ to work $45$ hours per week $($and all other parameters remained unchanged$),$ what would the company's profit be$?$

$($e$)$ If each unit of bookcase $2$ sold for $$10($and all other parameters remained unchanged$),$ what would be the optimal quantity of bookcase $2$ to produce$-$or can you not tell without resolving the LP$?$

$($f$)$ Reconsider the All$-$Balsa problem formulation and suppose that instead of having $400bf$ of raw material available at $$\frac{1\mathrm{.}50}{b}f,$ All$-$Balsa faces a two$-$tier pricing scheme such that the first $200b\frac{f}{?}$ week costs $$\frac{2\mathrm{.}00}{b}f,$ but any rount above $200b\frac{f}{?}$ week up to a