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 selll 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 selll 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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