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 – ; 125 , its production cost per unit is US$5.00 and its fixed cost are the same as for company A.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question

Answer Question (iv) to (x) (picture two). The problem question is on the first picture. 

 

Problem 1
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 -D5 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.
(iii) Derive the profit function, II(x) for company A.
Transcribed Image Text:Problem 1 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 -D5 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. (iii) Derive the profit function, II(x) for company A.
(iv) Using a spreadsheet, create a table for showing x, R(x)a, 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:(iv) Using a spreadsheet, create a table for showing x, R(x)a, 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.
Expert Solution
steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,