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Chapter 2: Problem 14

Lorne has determined the fixed cost of producing his new invention is \(N\) dollars. The variable cost is \(\$ 10.75\) per item. What is the average cost per item of producing \(W\) items?

Short Answer

Expert verified
The average cost per item of producing \(W\) items is \((N + 10.75W)/W\) dollars

Step by step solution

01

Definition of Average Cost

The average cost is calculated by dividing the total cost of production by the number of items produced. In this case, the total cost of production is the sum of the fixed cost and the variable cost of the items produced.
02

Calculate Total Cost

Calculate the total cost of producing \(W\) items by adding the fixed cost \(N\) to the product of the variable cost per item (\$10.75) and the number of items produced (\(W\)). The formula to use is: Total Cost = Fixed Cost + (Variable Cost per Item)*(Number of Items Produced), or Total Cost = \(N + 10.75W\) in this case.
03

Calculate Average Cost

Divide the total cost calculated in the previous step by the number of items produced (\(W\)) to find the average cost per item. The formula to use is: Average Cost = Total Cost/Number of Items Produced, or Average Cost = \((N + 10.75W)/W\) in this case.

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Key Concepts

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

Fixed Cost
Fixed cost is a crucial concept in understanding how production costs are structured. This expense remains constant regardless of how many units are produced. Whether you make one item or a thousand, this cost doesn't change. It usually includes things like rent, salaries of permanent staff, or machinery that doesn't need frequent replacement.

In Lorne's scenario, the fixed cost is given as \( N \) dollars. This amount is paid no matter how many items Lorne decides to produce. Understanding fixed costs helps businesses plan their budget since these expenses are predictable and uniform across all levels of production.
Variable Cost
Variable costs, unlike fixed costs, fluctuate depending on the level of production. They are the costs incurred for each item produced and can include materials, labor directly used in production, or utility costs tied to operation hours.

For Lorne, the variable cost is set at \\(10.75 per item. This means that for every additional item produced or sold, an extra \\)10.75 needs to be accounted for in the cost structure. Variable costs are vital for price-setting and assessing how changes in production volumes impact overall expenses.
Cost per Item
Calculating the cost per item is essential for understanding how efficiently a business can produce its goods. The cost per item helps determine the pricing strategy and ensure profitability.

To find this average, you'll divide the total production cost by the number of items produced. In Lorne's case, the formula would look like this: Average Cost = \((N + 10.75W)/W\). Here, \( N \) is the fixed cost, \( 10.75W \) represents the total variable cost for producing \( W \) items, and dividing by \( W \) gives the cost per item.
  • Total Cost: Sum of fixed and variable costs.
  • Number of Items: Total output (\( W \)).
By understanding the cost per item, businesses can make informed decisions on pricing and production strategies.
Production Cost Analysis
Production cost analysis is a method used to evaluate all costs involved in creating a product. It breaks down the expenses into fixed and variable categories, allowing for a comprehensive view of the financial outlay needed for production.

In Lorne's exercise, calculating the total cost involves considering both the fixed cost \( N \) and the variable cost of \$10.75 per item over \( W \) items. Analyzing these costs together can reveal important insights:
  • Efficiency: Are you using resources wisely to keep costs low?
  • Scalability: How do costs change with varying levels of production?
  • Profitability: At what production level does your business break even or make a profit?
Effective production cost analysis helps in identifying areas for cost savings and ensures a competitive edge in pricing and profitability. It is a vital tool for making strategic decisions in business growth and operations.

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Most popular questions from this chapter

A jewelry manufacturer has determined the expense equation for necklaces to be \(E=1,250 q+800,000\) , where \(q\) is the quantity demanded. At a particular price, the breakeven revenue is \(\$ 2,600,000\) . a. What is the quantity demanded at the breakeven point? b. If the breakeven revenue changes to 3.5 million, will the quantity demanded have increased or decreased? Explain.

Use the following situation to answer Exercises 4鈥�20. A company produces a security device known as Toejack. Toejack is a computer chip that parents attach between the toes of a child, so parents can track the child鈥檚 location at any time using an online system. The company has entered into an agreement with an Internet service provider, so the price of the chip will be low. Set up a demand function鈥攁 schedule of how many Toejacks would be demanded by the public at different prices. The horizontal axis represents price, and the vertical axis represents quantity. Does the demand function have a positive or negative slope? Explain.

Green yard鈥檚 manufactures and sells yard furniture made out of recycled materials. It is considering making a lawn chair from recycled aluminum and fabric products. The expense and revenue functions are \(E=-1,850 p+800,000\) and \(R=-100 p^{2}+20,000 p.\) a. Determine the profit function. b. Determine the price, to the nearest cent, that yields the maximum profit. c. Determine the maximum profit, to the nearest cent.

In a鈥揹, each set of bivariate data has a causal relationship. Determine the explanatory and response variables for each set of data. a. height and weight of a student b. grade on a math test and number of hours the student studied c. number of hours worked and paycheck amount d. number of gallons of gas consumed and weight of a car

The expense function for the Wonder Widget is \(E=4.14 q+55,789 .\) a. What is the fi xed cost in the expense function? b. What is the cost of producing 500 Wonder Widgets? c. What is the average cost per widget of producing 500 Wonder Widgets? Round to the nearest cent. d. What is the total cost of producing 600 Wonder Widgets? e. What is the average cost per widget of producing 600 Wonder Widgets? Round to the nearest cent. f. As the number of widgets increased from 500 to 600, did the average expense per widget increase or decrease? g. What is the average cost per widget of producing 10,000 Wonder Widgets? Round to the nearest cent.
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