/*! 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 2 For Activities 1 through \(4,\) ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

For Activities 1 through \(4,\) rewrite the statements into equivalent statements without using the term marginal. When weekly sales are 150 units, marginal profit is \(\$ 4.75\) per unit.

Short Answer

Expert verified
When weekly sales increase from 150 to 151 units, the profit increases by \(\$4.75\)."

Step by step solution

01

Understand the Term 'Marginal Profit'

The term 'marginal profit' refers to the additional profit gained from the sale of one more unit. In this context, marginal profit of \(\\(4.75\) per unit means that each additional unit sold contributes \(\\)4.75\) to the overall profit.
02

Rewrite Without 'Marginal'

To express the statement without using the term 'marginal', it can be rewritten as: 'When weekly sales increase from 150 to 151 units, the profit increases by \(\$4.75\).' This captures the essence of marginal profit without using the specific term.

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 91Ó°ÊÓ!

Key Concepts

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

Additional Profit
When discussing 'additional profit', we're thinking about the extra income a company makes from producing and selling one more unit of a product. It's a way to measure how beneficial each new sale is to the company's overall profit.

Let's say a business is considering increasing its production. The decision to produce and sell one more unit would depend on whether the extra unit increases the profits. This increase in profits—whether it's a dollar or more per item—is what's called the additional profit.

In practice, understanding additional profit helps companies adjust their production levels strategically. Companies aim to increase production only if the additional profit outweighs the additional costs involved. This mindset helps to optimize resources efficiently.
sales increase
Sales increase refers to a rise in the number of units a business sells over a specific period. It's an important factor for any company, as increasing sales often leads to higher profits—providing other factors, like production costs, remain stable.

In the context of marginal profit, if a business sells 150 units and decides to increase sales to 151 units, the focus is on understanding how this slight increase in sales affects profits. If the additional unit sold results in an extra profit, it's a good indicator of a beneficial sales increase.

Companies use sales increase analysis to project future growth and understand consumer demand. Sometimes, a controlled sales increase—not too fast, not too slow—can stabilize company growth and lead to long-term success.
profit per unit
Profit per unit is a key financial metric that tells us how much profit the company makes from selling each individual product. It’s calculated by taking the selling price and subtracting all relevant costs like production and operational expenses associated with making that unit.

For instance, if a company sells a product for $20 and the costs involved are $15, the profit per unit is $5. This means for each unit sold, the company earns $5 which contributes to the overall profit.

In practical terms, knowing the profit per unit helps managers make critical decisions about pricing, product design, and cost reduction strategies. It ensures that each unit sold adds positively to the company’s bottom line, thereby supporting financial sustainability.

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

Natural Gas Price The average price (per 1000 cubic feet) of natural gas for residential use can be modeled as $$ p(x)=0.0987 x^{4}-2.1729 x^{3}+17.027 x^{2}-55.023 x $$ +72.133 dollars where \(x\) is the number of years since 2000 , data from \(3 \leq x \leq 8\) (Source: Based on data from Energy Information Administration's Natural Gas Monthly, October 2008 and August 2009\()\) a. Locate the two inflection points on the interval \(4

For Activities 5 through \(10,\) given the units of measure for production and the units of measure for cost or revenue a. Write the units of measure for the indicated marginal. b. Write a sentence interpreting the marginal as an increase. Revenue is given by \(R(q)\) thousand dollars when \(q\) hundred units are sold; \(R^{\prime}(16)=0.15 .\)

For Activities 7 through \(18,\) write the first and second derivatives of the function. \(L(t)=\frac{100}{1+99.6 e^{-0.02 t}}\)

The body-mass index (BMI) of an individual who weighs \(w\) pounds and is \(h\) inches tall is given as $$ B=703 \frac{w}{b^{2}} $$ (Source: \(C D C\) a. Write an equation showing the relationship between the body-mass index and the height of a young teenager who weighs 100 pounds. b. Construct a related-rates equation showing the interconnection between the rates of change with respect to time of the body-mass index and the height. c. If the weight of the teenager who is 5 feet 3 inches tall remains constant at 100 pounds while she is growing at a rate of \(\frac{1}{2}\) inch per year, how quickly is her body-mass index changing?

a. Graph \(g, g^{\prime}\), and \(g^{\prime \prime}\) between \(x=0\) and \(x=15 .\) Indicate the relationships among points on the three graphs that correspond to maxima, minima, and inflection points. b. Calculate the input and output of the inflection point on the graph of \(g .\) Is it a point of most rapid decline or least rapid decline? \(g(x)=0.04 x^{3}-0.88 x^{2}+4.81 x+12.11\)

See all solutions

Recommended explanations on Math Textbooks

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.