Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A company produces a special new type of TV. The company has fixed costs of $493,000, and it costs $1200 to produce each TV. The company projects that if it charges a price of $2400 for the TV, it will be able to sell 800 TVs. If the company wants to sell 850 TVs, however, it must lower the price to $2100. Assume a linear demand. What are the company's profits if marginal profit is $0? The profit will $. (Round answer to nearest cent.)

A company produces a special new type of TV. The company has fixed costs of $493,000, and it costs $1200 to produce each TV. The company projects that if it charges a price of $2400 for the TV, it will be able to sell 800 TVs. If the company wants to sell 850 TVs, however, it must lower the price to $2100. Assume a linear demand. What are the company's profits if marginal profit is $0? The profit will $. (Round answer to nearest cent.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
Question
100%
Help
**Understanding Profit Calculation for a Special Type of Television** This scenario involves a company that produces a special new type of TV. The following financial details are given: - Fixed costs: $493,000 - Production cost per TV: $1200 - Selling price if 800 TVs are sold: $2400 per TV - Selling price if 850 TVs are sold: $2100 per TV The task is to determine the company's profits when the marginal profit is $0, with the assumption of a linear demand. **Step-by-Step Breakdown:** 1. **Calculation of Revenue:** - If the company charges $2400 per TV, it will sell 800 TVs. - If the company lowers the price to $2100 per TV, it will sell 850 TVs. Let's derive the demand function assuming it is linear: Q (quantity) = a - bP (price), where: a and b are constants, For 800 TVs at $2400: 800 = a - b(2400), For 850 TVs at $2100: 850 = a - b(2100). Solving these equations simultaneously will give us the values of a and b: From 800 = a - 2400b, a = 800 + 2400b Substitute this into 850 = a - 2100b: 850 = 800 + 2400b - 2100b 850 = 800 + 300b 50 = 300b b = 50/300 b = 1/6 Substitute b back into a = 800 + 2400b, a = 800 + 2400(1/6), a = 800 + 400, a = 1200. Hence, the demand function is Q = 1200 - (1/6)P. 2. **Calculation of Profit:** - Total Revenue (TR) = Price (P) * Quantity (Q). - Total Cost (TC) = Fixed Costs + Variable Costs, where Variable Costs = Cost per TV * Quantity. Marginal profit is determined by the change in profit with respect to the change in quantity produced. Profit (π) = TR - TC = (Price * Quantity)
Transcribed Image Text:**Understanding Profit Calculation for a Special Type of Television** This scenario involves a company that produces a special new type of TV. The following financial details are given: - Fixed costs: $493,000 - Production cost per TV: $1200 - Selling price if 800 TVs are sold: $2400 per TV - Selling price if 850 TVs are sold: $2100 per TV The task is to determine the company's profits when the marginal profit is $0, with the assumption of a linear demand. **Step-by-Step Breakdown:** 1. **Calculation of Revenue:** - If the company charges $2400 per TV, it will sell 800 TVs. - If the company lowers the price to $2100 per TV, it will sell 850 TVs. Let's derive the demand function assuming it is linear: Q (quantity) = a - bP (price), where: a and b are constants, For 800 TVs at $2400: 800 = a - b(2400), For 850 TVs at $2100: 850 = a - b(2100). Solving these equations simultaneously will give us the values of a and b: From 800 = a - 2400b, a = 800 + 2400b Substitute this into 850 = a - 2100b: 850 = 800 + 2400b - 2100b 850 = 800 + 300b 50 = 300b b = 50/300 b = 1/6 Substitute b back into a = 800 + 2400b, a = 800 + 2400(1/6), a = 800 + 400, a = 1200. Hence, the demand function is Q = 1200 - (1/6)P. 2. **Calculation of Profit:** - Total Revenue (TR) = Price (P) * Quantity (Q). - Total Cost (TC) = Fixed Costs + Variable Costs, where Variable Costs = Cost per TV * Quantity. Marginal profit is determined by the change in profit with respect to the change in quantity produced. Profit (π) = TR - TC = (Price * Quantity)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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,
SEE MORE TEXTBOOKS