Task Type: Individual Project Deliverable Length: 3 Parts: See Assignment Details
Points Possible: 150 Due Date: 11/5/2012 11:59:59 PM CT
Weekly tasks or assignments (Individual or Group Projects) will be due by Monday and late submissions will be assigned a late penalty in accordance with the late penalty policy found in the syllabus. NOTE: All submission posting times are based on midnight Central Time.
Task Background
This Individual Project assignment serves as a summary of the key learning over the past 4 weeks of the course and includes some research for you to help you prepare for what is still to come in the last week of the class. In this course, you have focused on the fundamentals of mathematics and how these topics relate to real-world applications.
Scenario: In this assignment, you are the entrepreneur investing in a specialty pizza restaurant, and you are required to apply what you have learned in your business algebra math course given various scenarios.
Please be prepared to discuss this assignment for the Week 4 Discussion Board.
Assignment
Part I: Previously, when equations and inequalities were covered, you found many uses of various equations and inequalities and how they can be applied in real-world settings. In 2 paragraphs, discuss the following:
a. How can equations and inequalities help a business maximize profit or minimize costs?
b. What is the importance of understanding how to set up and solve equations and inequalities (discuss in general without a mathematical example)?
Part II
Break-Even Analysis: A Look at Profit and Loss: As an entrepreneur, there are going to be many decisions that you need to make, such as the price to charge your customers for your goods and services. You have just graduated from college and recently opened a specialty pizza restaurant. Based on surveys conducted in your area, you determine that it is feasible to sell your specialty pizzas for $15. The cost for making the pizzas includes a fixed cost of $55 and a labor cost of $4 per pizza.
a. Establish an equation to determine revenue.
b. Establish an equation to determine total cost.
c. How many pizzas must be sold to break even (i.e., you experience neither a profit nor a loss)? Interpret your result.
As a business owner, it is very important to have an understanding of profit and loss. The formula for determining profit is Profit = revenue – cost (P = R – C).
d. Determine the profit if 500 specialty pizzas are sold. Interpret your result.
e. How many specialty pizzas would need to be sold to make a profit of $1,100? Interpret your result.
f. How many specialty pizzas would you need to sell if you wanted to make a profit greater than $1,595? Interpret your result.
Part I:
a. Equations and inequalities can help a business maximize profit or minimize costs by providing a mathematical framework for decision-making. For example, a business can use equations to model the relationship between price and quantity sold, allowing them to determine the optimal price point that maximizes revenue. Inequalities can be used to set constraints, such as minimum production levels or maximum production costs, helping the business minimize costs and avoid inefficiencies. Overall, equations and inequalities provide a systematic approach to analyzing and optimizing business operations.
b. Understanding how to set up and solve equations and inequalities is important for several reasons. Firstly, it allows businesses to quantify and measure different variables and their relationships, enabling them to make informed decisions based on data and evidence. Secondly, solving equations and inequalities provides a means of testing different scenarios and analyzing the impact of changing variables. This helps businesses evaluate different strategies and make predictions about future outcomes. Lastly, mathematical modeling through equations and inequalities fosters critical thinking and problem-solving skills, which are valuable for business professionals in general. Learning how to apply mathematical concepts to real-world situations helps develop logical reasoning and analytical abilities.
Part II:
a. The equation to determine revenue can be established by multiplying the price per pizza ($15) by the number of pizzas sold (x): Revenue = 15x.
b. The equation to determine total cost can be established by summing the fixed cost ($55) with the labor cost per pizza ($4) multiplied by the number of pizzas sold (x): Total Cost = 55 + 4x.
c. To break even, the revenue should equal the total cost. By setting the revenue equation equal to the total cost equation and solving for x, you can determine the number of pizzas that need to be sold to break even: 15x = 55 + 4x. This equation can be rearranged to isolate x: 11x = 55. Dividing both sides by 11 gives x = 5.
Interpretation: To break even, the business needs to sell 5 specialty pizzas. This means that the revenue generated from selling 5 pizzas will cover all the costs, resulting in neither a profit nor a loss.
d. To determine the profit when 500 specialty pizzas are sold, you can substitute 500 into the revenue and cost equations: Profit = Revenue - Cost = (15 * 500) - (55 + 4*500). Simplifying this equation gives Profit = 7500 - 2555 = 4945.
Interpretation: The profit from selling 500 specialty pizzas is $4945.
e. To determine the number of specialty pizzas needed to make a profit of $1100, you can set up the profit equation (P = Revenue - Cost) and solve for x: 1100 = 15x - (55 + 4x). Simplifying this equation gives 11x = 1155. Dividing both sides by 11 gives x ≈ 105.
Interpretation: To make a profit of $1100, the business needs to sell approximately 105 specialty pizzas.
f. To determine the number of specialty pizzas needed to make a profit greater than $1595, you can set up the profit equation (P = Revenue - Cost) and solve for x: 1595 < 15x - (55 + 4x). Simplifying this inequality gives 1595 < 11x - 55. Add 55 to both sides gives 1650 < 11x. Dividing both sides by 11 gives x > 150.
Interpretation: To make a profit greater than $1595, the business needs to sell more than 150 specialty pizzas.