d) Assume that the cost function is linear. Use the financial department's estimates to express the cost function in terms of x.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 21T: A manufacturer produces two models of television stands. The table at the left shows the times (in...
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Parts D-Fonly

CASE STUDY 2
A local company is planning to manufacture and market a four-slice toaster. For this toaster, the
research department's estimates are a weekly demand of 300 toasters at a price of $25 per toaster
and a weekly demand of 400 toasters at a price of $20. The financial department's estimates are fixed
weekly costs of $5,000 and variable costs of $5 per toaster.
a) Assume that the relationship between price p and demand x is linear. Use the research
department's estimates to express p as a function of x and determine the domain of the
function.
b) Using your knowledge from Finite Math, determine the Revenue function in terms of x.
c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500
units. Interpret these results. (HINT: Consider what a positive or negative first derivative
implies)
d) Assume that the cost function is linear. Use the financial department's estimates to express the
cost function in terms of x.
e) Determine the Marginal cost and interpret the results.
f) Explain why performing Marginal Analysis will help the company to make good business
decisions. (Approximately 250 words)
COMMON FORMULAS:
y2-y1
1. т %3D
X2-x1
2. у 3D тх + b
3. R(x) = x * p(x)
Transcribed Image Text:CASE STUDY 2 A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department's estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department's estimates are fixed weekly costs of $5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price p and demand x is linear. Use the research department's estimates to express p as a function of x and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of x. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department's estimates to express the cost function in terms of x. e) Determine the Marginal cost and interpret the results. f) Explain why performing Marginal Analysis will help the company to make good business decisions. (Approximately 250 words) COMMON FORMULAS: y2-y1 1. т %3D X2-x1 2. у 3D тх + b 3. R(x) = x * p(x)
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