If company A manufactures t-shirts and sells them to retailers for US$9.80 each.

It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30.CompanyB also manufactures t-shirtsand sell them directly to consumers.The demand for its product is p= 15 - x/125 its production cost per unit is US$5.00 and its fixed cost are the same as for company A .

(i)Derive the total revenue function, R(x) for company A.

(i)Derive the total cost function, C(x) for company A.

(i)Derive the profit function, (x) for company A.

(i)Using a spreadsheet, make a table for showing x, R(x)_?, C(x)for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.

(i)Graph the functions from (d) above on the same axe

(i)From your graph, determine the break-even level of output for company A.

(i)Derive the total revenue function, R(x) for company B.

(i)Derive the profit function, (x) for company B.

(i)How many t-shirts must company B sell to in order to break-even.

(i)How many t-shirts must company B sell to maximise its profit.