A shoes manufacturer has determined that the production cost for each pair of shoes is $$15$ and the fixed cost is $$30,000.$ Each pair of shoes sells for $$35.$

a$)$ Write the Total Cost function $T$ C$.$

b$)$ Write the Total Revenue function $TR.$

c$)$ Find the number of pair of shoes and their price that should be sold to Break$-$Even.

d$)$ Draw the graph of the Cost and Revenue functions.

e$)$ Find the Profit$/$Loss if $1,000$ pair of shoes are sold.

f$)$ How many pair of shoes should be sold to gain a profit of $$12,000?$