A small business makes handcrafted lamps. The fixed cost for production setup is $$500,$ and the variable cost to produce each lamp is $$20.$ In the first week of operation they sold $13$ and accumulated $$585$ in revenue. A week later they sold $38$ lamps and accumulated $$1710.$ Letting P $=$ Profit, C $=$ Cost, R $=$ Revenue, and x $=$ number of lamps:

a$.$ The Revenue function is

Question Blank $1$ of $7$

b$.$ The Cost function is

Question Blank $2$ of $7$

c$.$ The Profit function is

Question Blank $3$ of $7$

d$.$ The shop only has enough storage space for $500$ lamps. Assuming maximum storage capacity on a given day, what is the maximum profit they could accrue on that day? $

Question Blank $4$ of $7$

e$.$ How many lamps need to be sold to achieve a profit of $$1000.$

Question Blank $5$ of $7$

lamps

f$.$ How many lamps must be sold to break even?

Question Blank $6$ of $7$

lamps

g$.$ If the cost to produce a lamp went up to $$30,$ how would the break even quantity be impacted?

Question Blank $7$ of $7$