t has fixed costs of $2625 related to the production of the t-shirts, and the production cost per nit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers. "he demand for its product is p = 15 – 125 its production cost per unit is US$5.00 nd its fixed cost are the same as for company A.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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Chapter17: Long-term Investment Analysis
Section: Chapter Questions
Problem 10E
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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 Balso manufactures t-shirts and selll them directly to consumers.
The demand for its product is p = 15 -
125
. its production cost per unit is US$5.00
and its fixed cost are the same as for company A.
(1) Derive the total revenue function, R(x) for company A.
(ii) Derive the total cost function, C(x) for company A.
(ii) Derive the profit function, II(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, II(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.
Transcribed Image Text: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 Balso manufactures t-shirts and selll them directly to consumers. The demand for its product is p = 15 - 125 . its production cost per unit is US$5.00 and its fixed cost are the same as for company A. (1) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (ii) Derive the profit function, II(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, II(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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