f 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. Company B also manufactures t-shirts and 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. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, Π(x) for company A.
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. Company B also manufactures t-shirts and 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.
(ii) Derive the total cost function, C(x) for company A.
(iii) Derive the profit function, Π(x) for company A.
(iv) Using a spreadsheet, create 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.
(v) Graph the functions from (d) above on the same axes.
(vi) From your graph, determine the break-even level of output for company A.
(vii) Derive the total revenue function, R(x) for company B.
(viii) Derive the profit function, Π(x) for company B.
(ix) How many t-shirts must company B sell to in order to break-even.
(x) How many t-shirts must company B sell to maximise its profit.
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