$5$A$.$ You work for a firm that makes tables. Your company makes $2$ types of tables that sell equally well for the same price, and you can always sell as many as you can make. Each month your firm can make $100$ tables of either type or a combination of the two. Type A takes $5$ units of wood and $1$ unit of metal and Type B uses $2$ units of wood and $3$ units of metal. Assume each unit of wood costs $$20$ and each unit of metal costs $$15.$ Assume it costs $$1,$ unit$/$mile to ship wood and $$2/$unit$/$mile to ship metal, and $$5/$table$/$mile to ship your final product. Your current location $($Site A$)$ is $100$ miles from where you get wood, $60$ miles from where you get metal and $40$ miles from the market.

$(2$ points$)$ How many of each table are you going to make each month at these costs?

$(1$ point$)$ What's the lowest homemade cost for tables that would leave your business viable in this market?

$5$B$.(3$ points$)$ Suppose there's a new site available $($Site B$)$ that's the same distance from the market but $60$ miles from where you get wood and $100$ miles from where you get metal. Will you move? If yes, what's the most you'd be willing to pay in relocation costs? if no$,$ how much would you need in government incentives beyond relocation costs to move? What assumptions did you use when making this decision? $($Both relocation costs and government incentives are up$-$front, one$-$time amounts.$)$