/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 If the current price is \(\$ 50\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 27

If the current price is \(\$ 50\) and you find that profit is maximized when there are -3 price reductions of \(\$ 5,\) what should the price be?

Short Answer

Expert verified
The price should be $35.

Step by step solution

01

Understanding the Problem

The problem states that the current price is $50. We are told that the profit is maximized after 3 price reductions. These reductions are $5 each. Our task is to find the price after these reductions.
02

Calculating the Total Reduction

To find the total reduction, we must multiply the number of reductions by the amount reduced each time. Since there are 3 reductions of $5 each, we calculate it as: Total Reduction = 3 reductions 脳 $5/reduction = $15.
03

Determining the New Price

To find the new price after the reductions, we need to subtract the total reduction from the current price. New Price = Current Price - Total Reduction = $50 - $15 = $35.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Price Reduction
Price reduction refers to the process of lowering the selling price of an item or service. This can be done for various reasons, such as boosting sales, clearing out inventory, or reaching profit maximization.
In the context of the given exercise, we learned that each price reduction was $5. A price reduction can be strategic, especially when aimed at reaching the point of maximum profit.
  • Each reduction amount ( $5) is subtracted multiple times according to the number of reductions.
  • It directly impacts the final selling price, which in turn affects the profit margins.
  • Understanding the optimal number of price reductions is crucial for reaching desired financial outcomes.
Frequent price reductions can lead to different market implications, such as increased attractiveness to price-sensitive consumers or potential perceptions of lower product value.
Current Price
The current price is the original price at which an item or service is being sold before any modifications, such as reductions, are made. It is a crucial starting point in determining the effects of any price changes on profit and sales.
In the exercise, the current price is given as $50. This amount serves as the baseline from which we calculate any further changes to determine the maximum profit state.
  • The current price can be influenced by market dynamics and cost structures.
  • It's important for businesses to know their starting point to accurately assess the impact of strategic decisions like price reductions.
  • A clear understanding of current pricing helps set realistic targets for profit maximization.
Keeping an eye on the initial pricing and making strategic decisions around it can support competitive positioning and financial well-being.
New Price
The new price is the adjusted selling price after making changes such as price reductions. It is the final price that customers will see and be charged.
In our exercise, the new price is calculated by subtracting the total reduction ( $15) from the current price ( $50), resulting in $35.
  • The new price can significantly affect sales volume and profitability.
  • Consumers often perceive the new price as representing the true value of the item or service.
  • New pricing strategies should be evaluated for how they align with overall business goals.
It is important to not only calculate but also consider the implications of the new price for maintaining a balance between competitiveness and profitability.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A company's cost function is $$ C(x)=x^{2}+2 x+4 $$ dollars, where \(x\) is the number of units. a. Enter the cost function in \(y_{1}\) on a graphing calculator. b. Define \(y_{2}\) to be the marginal cost function by defining \(y_{2}\) to be the derivative of \(y_{1}\) (using NDERIV). c. Define \(y_{3}\) to be the company's average cost function, $$A C(x)=\frac{C(x)}{x}$$ by defining \(y_{3}=\frac{y_{1}}{x}\). d. Turn off the function \(y_{1}\) so that it will not be graphed, but graph the marginal cost function \(y_{2}\) and the average cost function \(y_{3}\) on the window [0,10] by \([0,10] .\) Observe that the marginal cost function pierces the average cost function at its minimum point (use TRACE to see which curve is which function). e. To see that the final sentence of part (d) is true in general, change the coefficients in the cost function \(C(x),\) or change the cost function to a cubic or some other function [so that \(C(x) / x\) has a minimum]. Again turn off the cost function and graph the other two to see that the marginal cost function pierces the average cost function at its minimum.

In general, implicit differentiation gives an expression for the derivative that involves both \(x\) and \(y\). Under what conditions will the expression involve only \(x ?\)

Find the linear approximation to each function and evaluate it at the given values of \(x\) and \(d x\). \(\frac{1}{x}\) at \(x=5\) and \(d x=1\)

The number \(x\) of bacteria of type \(X\) and the number \(y\) of type \(Y\) that can coexist in a cubic centimeter of nutrient are related by the equation \(2 x y^{2}=4000\). Find \(d y / d x\) at \(x=5\) and interpret your answer.

\(37-40 .\) Find the equation of the tangent line to the curve at the given point using implicit differentiation. Elliptic curve \(y^{2}=x^{3}-4 x+1\) at (-2,1) (See diagram in next column.)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.