/*! 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 77 The revenue and cost equations f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 77

The revenue and cost equations for a product are \(R=x(75-0.0005 x)\) and \(C=30 x+250,000,\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 750,000 ?\) What is the price per unit?

Short Answer

Expert verified
The calculations for the exact number of units that need to be sold and the price per unit are dependent on the specifics of the solution to the inequality and therefore cannot be answered directly here. Generally, two tasks need to be performed to answer these questions: Firstly, the inequality has to be solved algebraically for \(x\). Secondly, \(x\) has to be put into the revenue function and the resulting \(R\) divided by \(x\).

Step by step solution

01

Set up the profit equation

Profit is calculated as revenue minus cost. Using the given equations for revenue (\(R=x(75-0.0005 x)\)) and cost (\(C=30x+250,000\)), the profit (\(P\)) can be calculated by the equation \(P = R - C\). Integrating the given equations into this formula leads to \(P = x(75-0.0005x) - (30x+250,000)\).
02

Calculate the number of units for a profit of at least $750,000.

To find out how many units have to be sold to reach a profit of at least $750,000, set up an inequality: \(P \geq 750,000\). Solve this inequality (\(x(75-0.0005x) - (30x+250,000) \geq 750,000\)) for \(x\).
03

Calculate the price per unit

To find the price per unit, substitute the number of units obtained in step 2 into the revenue function \(R=x(75-0.0005 x)\). Solve this equation for \(R\), then divide \(R\) by \(x\) to get the price per unit.

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!

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) Find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. $$3 x^{2}+b x+10=0$$

Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-3 x^{3}-x^{2}-12 x-20\) (Hint: One factor is \(\left.x^{2}+4 .\right)\)

A bulk food storage bin with dimensions 2 feet by 3 feet by 4 feet needs to be increased in size to hold five times as much food as the current bin. (Assume each dimension is increased by the same amount.) (a) Write a function that represents the volume \(V\) of the new bin. (b) Find the dimensions of the new bin. PICTURE CANT COPY

Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=f(2 x)$$

Explore transformations of the form \(g(x)=a(x-h)^{5}+k\) (a) Use a graphing utility to graph the functions \(y_{1}=-\frac{1}{3}(x-2)^{5}+1\) and \(y_{2}=\frac{3}{5}(x+2)^{5}-3\) Determine whether the graphs are increasing or decreasing. Explain. (b) Will the graph of \(g\) always be increasing or decreasing? If so, then is this behavior determined by \(a, h,\) or \(k ?\) Explain. (c) Use the graphing utility to graph the function \(H(x)=x^{5}-3 x^{3}+2 x+1\) Use the graph and the result of part (b) to determine whether \(H\) can be written in the form \(H(x)=a(x-h)^{5}+k\) Explain.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

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.