Learn Before
Example: Translating and Solving a Profit Inequality for a Service Business
To determine the required hours of work to achieve a profit goal, translate the problem into an inequality. For example, if a pet sitting business charges $32 per hour, has monthly expenses of $2,272, and aims for a profit of at least $800, let be the number of hours worked. The profit inequality is . Adding to both sides yields . Dividing by gives . Therefore, at least 96 hours must be worked to earn the target profit.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Calculating Gains for the First Adopter of a New Technology
Profit = Revenue - Costs
Firm-Customer Interaction for Profit Maximization with a Differentiated Product
Local Cafe Profitability
A small bakery generated $5,000 in sales during a single month. In that same month, its expenses were: $1,500 for ingredients, $1,000 for rent, and $2,000 for employee salaries. What was the bakery's profit for the month?
A technology company, 'TechForward,' reported total sales of $2 million last year with production and operational expenses of $1.8 million. A competing company, 'InnovateNow,' reported total sales of $1.5 million with expenses of $1.1 million. Based on this information, 'TechForward' was the more profitable company last year.
To calculate a firm's profit, one must first correctly identify all sources of revenue and all costs. For a company that manufactures and sells furniture, match each financial item below to the correct category it belongs to for the purpose of calculating profit.
Analyzing Paths to Profitability for a Startup
A company reports total revenues of $750,000 for the year. If its profit for that same year was $200,000, its total costs must have been $____.
A t-shirt company currently generates $10,000 in monthly revenue with total costs of $7,000. The company is considering launching a new advertising campaign that is expected to increase revenue by 30%. However, the campaign itself will cost an additional $2,500 per month. Based on these figures, how would the advertising campaign affect the company's monthly profit?
Strategic Profit Analysis for a Manufacturing Firm
A toy company increased its total sales revenue from $500,000 in Year 1 to $600,000 in Year 2. This means the company's profit must have been higher in Year 2 than in Year 1.
Revenue Growth vs. Profit Growth
Example: Solving a Business Profit Application with a Linear Inequality
Example: Translating and Solving a Profit Inequality for a Service Business
Example: Translating and Solving a Profit Inequality for a Maintenance Business
Learn After
A pet sitting business owner uses the inequality to plan their monthly workload, where is the number of hours worked. Arrange the steps to solve this inequality for in the correct order.
A freelance photographer uses the inequality to calculate the number of hours () they must work to meet a monthly profit goal. In this model, what does the term represent?
A service business charges 45 per hour and has fixed monthly expenses of 1,500. To determine how many hours () they must work to reach a profit goal of at least 2,000, they use the inequality . Match each component of this inequality with the business concept it represents.
First Step in Solving Profit Inequalities
When a small business owner sets up the initial inequality to determine the required work hours () to achieve a specific profit target, they must add their fixed monthly expenses to their total hourly revenue.