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−x125,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
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−x125,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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